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In Combinatorial Public Projects, there is a set of projects that may be undertaken, and a set of self-interested players with a stake in the set of projects chosen. A public planner must choose a subset of these projects, subject to a resource constraint, with the goal of maximizing social welfare. Combinatorial Public Projects has emerged as one of the paradigmatic problems in Algorithmic Mechanism Design, a field concerned with solving fundamental resource allocation problems in the presence of both selfish behavior and the computational constraint of polynomial-time. We design a polynomial-time, truthful-in-expectation, (1-1/e)-approximation mechanism for welfare maximization in a fundamental variant of combinatorial public projects. Our results apply to combinatorial public projects when players have valuations that are matroid rank sums (MRS), which encompass most concrete examples of submodular functions studied in this context, including coverage functions, matroid weighted-rank functions, and convex combinations thereof. Our approximation factor is the best possible, assuming P != NP. Ours is the first mechanism that achieves a constant factor approximation for a natural NP-hard variant of combinatorial public projects.
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arxiv:1103.0041
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We study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. We show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.
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arxiv:1103.0061
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We present a procedure to construct (n+1)-Hom-Nambu-Lie algebras from n-Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n+k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions.
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arxiv:1103.0093
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In this paper the phonon self energy produced by anharmonicity is calculated using second order many body perturbation theory for all bcc, fcc and hcp transition metals. The symmetry properties of the phonon interactions are used to obtain an expression for the self energy as a sum over irreducible triplets, very similar to integration in the irreducible part of the Brillouin zone for one particle properties. The results obtained for transition metals shows that the lifetime is on the order of 10^10 s. Moreover the Peierls approximation for the imaginary part of the self energy is shown to be reasonable for bcc and fcc metals. For hcp metals we show that the Raman active mode decays into a pair of acoustic phonons, their wave vector being located on a surface defined by conservation laws.
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arxiv:1103.0137
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The first public release of long-cadence stellar photometric data collected by the NASA Kepler mission has now been made available. In this paper we characterise the red-giant (G-K) stars in this large sample in terms of their solar-like oscillations. We use published methods and well-known scaling relations in the analysis. Just over 70% of the red giants in the sample show detectable solar-like oscillations, and from these oscillations we are able to estimate the fundamental properties of the stars. This asteroseismic analysis reveals different populations: low-luminosity H-shell burning red-giant branch stars, cool high-luminosity red giants on the red-giant branch and He-core burning clump and secondary-clump giants.
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arxiv:1103.0141
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The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important model system for the high-$T_c$ superconductors based on cuprates. Using the technique of self-similar continuous unitary transformations we derive effective Hamiltonians for the charge motion in these ladders. The key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit. A real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space. From the effective Hamiltonians we calculate the dispersions for single holes. Further calculations will enable the calculation of the interaction of two holes so that a handle of Cooper pair formation is within reach.
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arxiv:1103.0162
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In this article, we study the set of all solutions of linear differential equations using Hurwitz series. We first obtain explicit recursive expressions for solutions of such equations and study the group of differential automorphisms of the set of all solutions. Moreover, we give explicit formulas that compute the group of differential automorphisms. We require neither that the underlying field be algebraically closed nor that the characteristic of the field be zero.
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arxiv:1103.0170
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Les feuilletages de Hirsch sont des feuilletages par surfaces de vari\'et\'es compactes ferm\'ees de dimension 3, dont la dynamique transverse est celle d'un endomorphisme du cercle de degr\'e strictement sup\'erieur \`a 1. Le but de cette note est de construire, \`a partir d'une g-mesure associ\'ee \`a un tel endomorphisme, une mesure harmonique sur le feuilletage de Hirsch correspondant, au sens de Lucy Garnett. Ceci nous permet de donner des exemples de m\'etriques riemanniennes sur le fibr\'e tangent du feuilletage de Hirsch, lisses le long des feuilles et continues transversalement, pour lesquelles il existe plusieurs mesures harmoniques. De tels exemples montrent que le r\'esultat d'unique ergodicit\'e obtenu par le premier auteur et Victor Kleptsyn pour les feuilletages transversalement conformes [GAFA, 2007, Vol. 17, No 4, 1043-1105] n'est valable que lorsque la m\'etrique riemannienne est H\"old\'erienne transversalement, mais pas juste continue.
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arxiv:1103.0177
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We formulate and study a model for inhomogeneous long-range percolation on $\Zbold^d$. Each vertex $x\in\Zbold^d$ is assigned a non-negative weight $W_x$, where $(W_x)_{x\in\Zbold^d}$ are i.i.d.\ random variables. Conditionally on the weights, and given two parameters $\alpha,\lambda>0$, the edges are independent and the probability that there is an edge between $x$ and $y$ is given by $p_{xy}=1-\exp\{-\lambda W_xW_y/|x-y|^\alpha\}$. The parameter $\lambda$ is the percolation parameter, while $\alpha$ describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there exists an infinite component and on graph distance between remote pairs of vertices. First, we show that the tail behavior of the degree distribution is related to the tail behavior of the weight distribution. When the tail of the distribution of $W_x$ is regularly varying with exponent $\tau-1$, then the tail of the degree distribution is regularly varying with exponent $\gamma=\alpha(\tau-1)/d$. The parameter $\gamma$ turns out to be crucial for the behavior of the model. Conditions on the weight distribution and $\gamma$ are formulated for the existence of a critical value $\lambda_c\in(0,\infty)$ such that the graph contains an infinite component when $\lambda>\lambda_c$ and no infinite component when $\lambda<\lambda_c$. Furthermore, a phase transition is established for the graph distances between vertices in the infinite component at the point $\gamma=2$, that is, at the point where the degrees switch from having finite to infinite second moment. The model can be viewed as an interpolation between long-range percolation and models for inhomogeneous random graphs, and we show that the behavior shares the interesting features of both these models.
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arxiv:1103.0208
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We prove that the set of solutions to the parabolic singular $p$-Laplace equation with Dirichlet boundary conditions on a bounded Lipschitz domain $\Omega$ for all space dimensions is continuous in the parameter $p\in [1,+\infty)$ and the initial data. The highly singular limit case p=1 is included. In particular, we show that the solutions $u_p$ converge strongly in $L^2(\Omega)$, uniformly in time, to the solution $u_1$ of the parabolic 1-Laplace equation as $p\to 1$.
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arxiv:1103.0229
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We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic dynamics of a system. We find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the case of additive and multiplicative noise. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. Using Kramers-Kronig theory, it is then possible to derive the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide a example of application of our results by considering the Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations.
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arxiv:1103.0237
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A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently by the first-named author.
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arxiv:1103.0255
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Cosmological neutrinos strongly affect the evolution of the largest structures in the Universe, i.e. galaxies and galaxy clusters. We use large box-size full hydrodynamic simulations to investigate the non-linear effects that massive neutrinos have on the spatial properties of cold dark matter (CDM) haloes. We quantify the difference with respect to the concordance LambdaCDM model of the halo mass function and of the halo two-point correlation function. We model the redshift-space distortions and compute the errors on the linear distortion parameter beta introduced if cosmological neutrinos are assumed to be massless. We find that, if not taken correctly into account and depending on the total neutrino mass, these effects could lead to a potentially fake signature of modified gravity. Future nearly all-sky spectroscopic galaxy surveys will be able to constrain the neutrino mass if it is larger than 0.6 eV, using beta measurements alone and independently of the value of the matter power spectrum normalisation. In combination with other cosmological probes, this will strengthen neutrino mass constraints and help breaking parameter degeneracies.
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arxiv:1103.0278
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We consider one loop graviton corrections to scalar field Green's functions in the de Sitter phase of an inflationary space-time, a topic relevant to the computation of cosmological observables beyond linear order. By embedding de-Sitter space into an ultraviolet complete theory such as M-theory we argue that the ultraviolet (UV) cutoff of the effective field theory should be taken to be fixed in physical coordinates, whereas the infrared (IR) cutoff is expanding as space expands. In this context, we demonstrate how to implement three different regularization schemes -- the brute force cutoff regularization, dimensional regularization and Pauli-Villars regularization -- obtaining the same result for the scalar propagator if we use any of the three regularization schemes.
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arxiv:1103.0285
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We studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. We had Raychaudhuri type equation for the expansion. Assuming the stringy strong energy condition and initial convergence, we induced the existence of singularity and got the same inequality equation of the string strong energy condition for both timelike and null stringy congruence. In this paper we want to study the twist and shear aspects of the stingy geodesic surface congruence. Under some natural conditions we derive the equations of the twist and the shear in terms of the expansion of the universe. In appendix we investigate the geodesic surface congruence of the null strings.
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arxiv:1103.0300
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We report on the observation of a spin texture in a cold exciton gas in a GaAs/AlGaAs coupled quantum well structure. The spin texture is observed around the exciton rings. The observed phenomena include: a ring of linear polarization, a vortex of linear polarization with polarization perpendicular to the radial direction, an anisotropy in the exciton flux, a skew of the exciton fluxes in orthogonal circular polarizations and a corresponding four-leaf pattern of circular polarization, a periodic spin texture, and extended exciton coherence in the region of the polarization vortex. The data indicate a transport regime where the spin polarization is locked to the direction of particle propagation and scattering is suppressed.
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arxiv:1103.0321
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In a recent Comment [arXiv: 1101.3980] Shalaby criticised our paper "Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory" [arXiv:1002.3253]. On examining his arguments, we find that there are serious flaws at almost every stage of his Comment. In view of space and time considerations, we point out the major flaws that render his arguments invalid. Essentially Shalaby is attempting to obtain our results from a variational principle and to find a physical interpretation of his calculation. The variational procedure that he uses is inapplicable, and his description of the physics is wrong. We thus refute his criticism on all levels.
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arxiv:1103.0338
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We present zero-field {\mu}SR measurements for LiY$_{1-x}$Ho$_{x}$F$_{4}$ samples with x = 0.0017, 0.0085, 0.0406, and 0.0855. We characterize the dynamics associated with the formation of the (F-{\mu}-F)$^{-1}$ complex by comparing our data to Monte Carlo simulations to determine the concentration range over which the spin dynamics are determined primarily by the Ho$^{3+}$-{\mu} interaction rather than the F-{\mu} interaction. Simulations show that F-{\mu}-F oscillations should evolve into a Lorentzian Kubo-Toyabe decay for an increasing static magnetic field distribution {\Gamma} (i.e., increasing x), but the data do not show this behavior, consistent with the recently reported existence of strong magnetic fluctuations in this system at low temperatures. Anisotropy in the field distribution is shown to cause small errors of order 10% from behavior predicted for an isotropic distribution. Finally, numerical calculations show that values of {\Gamma} calculated in the single ion limit greatly exceed the values extracted from curve fits, suggesting that strong correlations play an important role in this system.
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arxiv:1103.0344
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Viewing gravitational energy-momentum $p_G^\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\mu$ naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space ${\bf M}^{\sl 4}$. To extract its physical content the full gauge group is reduced to its Poincar\'e subgroup. The respective Poincar\'e gauge fields, field strengths and Poincar\'e-covariant field equations are obtained and point-particle source currents are derived. The resulting set of non-linear field equations coupled to point matter is solved in first order resulting in Lienard-Wiechert-like potentials for the Poincar\'e fields. After numerical identification of gravitational and inertial energy-momentum Newton's inverse square law for gravity in the static non-relativistic limit is recovered. The Weak Equivalence Principle in this approximation is proven to be valid and spacetime geometry in the presence of Poincar\'e fields is shown to be curved. Finally, the gravitational radiation of an accelerated point particle is calulated.
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arxiv:1103.0349
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One fundamental problem in the field of network coding is to determine the network coding capacity of networks under various network coding schemes. In this thesis, we address the problem with two approaches: matroidal networks and capacity regions. In our matroidal approach, we prove the converse of the theorem which states that, if a network is scalar-linearly solvable then it is a matroidal network associated with a representable matroid over a finite field. As a consequence, we obtain a correspondence between scalar-linearly solvable networks and representable matroids over finite fields in the framework of matroidal networks. We prove a theorem about the scalar-linear solvability of networks and field characteristics. We provide a method for generating scalar-linearly solvable networks that are potentially different from the networks that we already know are scalar-linearly solvable. In our capacity region approach, we define a multi-dimensional object, called the network capacity region, associated with networks that is analogous to the rate regions in information theory. For the network routing capacity region, we show that the region is a computable rational polytope and provide exact algorithms and approximation heuristics for computing the region. For the network linear coding capacity region, we construct a computable rational polytope, with respect to a given finite field, that inner bounds the linear coding capacity region and provide exact algorithms and approximation heuristics for computing the polytope. The exact algorithms and approximation heuristics we present are not polynomial time schemes and may depend on the output size.
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arxiv:1103.0358
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The numerical dimension is a numerical measure of the positivity of a pseudo-effective divisor $L$. There are several proposed definitions of the numerical dimension due to Nakayama (2004) and Boucksom et al. (2004). We prove the equality of these notions and give several additional characterizations. We also prove some new properties of the numerical dimension.
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arxiv:1103.0440
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Graphene ranks highly as a possible material for future high-speed and flexible electronics. Current fabrication routes, which rely on metal substrates, require post synthesis transfer of the graphene onto a Si wafer or in the case of epitaxial growth on SiC, temperatures above 1000 {\deg}C are required. Both the handling difficulty and high temperatures are not best suited to present day silicon technology. We report a facile chemical vapor deposition approach in which nano-graphene and few layer graphene is directly formed over magnesium oxide and can be achieved at temperatures as low as 325 {\deg}C.
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arxiv:1103.0497
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In the game of pegging, each vertex of a graph is considered a hole into which a peg can be placed. A pegging move is performed by jumping one peg over another peg, and then removing the peg that has been jumped over from the graph. We define the pegging number as the smallest number of pegs needed to reach all the vertices in a graph no matter what the distribution. Similarly, the optimal-pegging number of a graph is defined as the smallest distribution of pegs for which all the vertices in the graph can be reached. We obtain tight bounds on the pegging numbers and optimal-pegging numbers of complete binary trees and compute the optimal-pegging numbers of complete infinitary trees. As a result of these computations, we deduce that there is a tree whose optimal-pegging number is strictly increased by removing a leaf. We also compute the optimal-pegging number of caterpillar graphs and the tightest upper bound on the optimal-pegging numbers of lobster graphs.
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arxiv:1103.0516
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We analyze various quantum phases of ultracold bosonic atoms in a periodic one dimensional optical superlattice. Our studies have been performed using the finite size density matrix renormalization group (FS-DMRG) method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the superfluid phase coexisting with density oscillations for a certain range of parameters of the system.
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arxiv:1103.0523
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Integrated optics provides an ideal test bed for the emulation of quantum systems via continuous-time quantum walks. Here we study the evolution of two-photon states in an elliptic array of waveguides. We characterise the photonic chip via coherent-light tomography and use the results to predict distinct differences between temporally indistinguishable and distinguishable two-photon inputs which we then compare with experimental observations. Our work highlights the feasibility for emulation of coherent quantum phenomena in three-dimensional waveguide structures.
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arxiv:1103.0604
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We present the complete automation of the computation of one-loop QCD corrections, including UV renormalization, to an arbitrary scattering process in the Standard Model. This is achieved by embedding the OPP integrand reduction technique, as implemented in CutTools, into the MadGraph framework. By interfacing the tool so constructed, which we dub MadLoop, with MadFKS, the fully automatic computation of any infrared-safe observable at the next-to-leading order in QCD is attained. We demonstrate the flexibility and the reach of our method by calculating the production rates for a variety of processes at the 7 TeV LHC.
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arxiv:1103.0621
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Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. Linear models of regression lines are considered in the general case of correlated errors in X and in Y for heteroscedastic data. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases. In the limit of homoscedastic data, the results determined for functional models are compared with their counterparts related to extreme structural models. While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with a single exception. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in presence of large dispersion data.
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arxiv:1103.0628
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A polycrystalline sample of YNiGe3, being a non-magnetic isostructural counterpart to the unconventional pressure-induced superconductor CeNiGe3, was studied by means of specific heat and electrical resistivity measurements at temperatures down to 360 mK and in magnetic fields up to 500 Oe. The compound was found to exhibit an ambient-pressure superconductivity below Tc = 0.46 K. The superconducting state in YNiGe3 is destroyed by magnetic field of the order of 500 Oe.
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arxiv:1103.0635
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We call the Lie algebra of a Lie group with a left invariant pseudo-Riemannian flat metric pseudo-Riemannian flat Lie algebra. We give a new proof of a classical result of Milnor on Riemannian flat Lie algebras. We reduce the study of Lorentzian flat Lie algebras to those with trivial center or those with degenerate center. We show that the double extension process can be used to construct all Lorentzian flat Lie algebras with degenerate center generalizing a result of Aubert-Medina on Lorentzian flat nilpotent Lie algebras. Finally, we give the list of Lorentzian flat Lie algebras with degenerate center up to dimension 6.
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arxiv:1103.0650
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In light of the recent neutrino experiment results from Daya Bay and RENO Collaborations, we study phenomenology of neutrino mixing angles in the Type III seesaw model with an discrete $A_4 \times Z_2$ symmetry, whose spontaneously breaking scale is much higher than the electroweak scale. At tree level, the tri-bimaximal (TBM) form of the lepton mixing matrix can be obtained from leptonic Yukawa interactions in a natural way. We introduce all possible effective dimension-5 operators, invariant under the Standard Model gauge group and $A_4 \times Z_2$, and explicitly show that they induce a deviation of the lepton mixing from the TBM mixing matrix, which can explain a large mixing angle $\theta_{13}$ together with small deviations of the solar and atmospheric mixing angles from the TBM. Two possible scenarios are investigated, by taking into account either negligible or sizable contributions from the light charged lepton sector to the lepton mixing matrix. Especially it is found in the latter scenario that all the neutrino experimental data, including the recent best-fit value of $\theta_{13} = 8.68^{\circ}$, can be accommodated. The leptonic CP violation characterized by the Jarlskog invariant $J_{CP}$ has a non-vanishing value, indicating a signal of maximal CP violation.
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arxiv:1103.0657
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We prove a generalization of the theorem which is proved by Fernandez, Ibanez, and de Leon. By this result, we give examples of non-K\"ahler manifolds which satisfy the property of compact K\"ahler manifolds concerning the coeffective cohomology.
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arxiv:1103.0703
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We initiate the study of the spherically symmetric Einstein-Klein-Gordon system in the presence of a negative cosmological constant, a model appearing frequently in the context of high-energy physics. Due to the lack of global hyperbolicity of the solutions, the natural formulation of dynamics is that of an initial boundary value problem, with boundary conditions imposed at null infinity. We prove a local well-posedness statement for this system, with the time of existence of the solutions depending only on an invariant H^2-type norm measuring the size of the Klein-Gordon field on the initial data. The proof requires the introduction of a renormalized system of equations and relies crucially on r-weighted estimates for the wave equation on asymptotically AdS spacetimes. The results provide the basis for our companion paper establishing the global asymptotic stability of Schwarzschild-Anti-de-Sitter within this system.
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arxiv:1103.0712
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We examine the problem of the collapse and fragmentation of molecular clouds with a Gaussian density distribution with high resolution, double precision numerical simulations using the GADGET-2 code. To describe the thermodynamic properties of the cloud during the collapse -to mimic the rise of temperature predicted by radiative transfer- we use a barotropic equation of state that introduces a critical density to separate the isothermal and adiabatic regimes. We discuss the effects of this critical density in the formation of multiple systems. We confirm the tendency found for Plummer and Gaussian models that if the collapse changes from isothermal to adiabatic at earlier times that occurs for the models with a lower critical density, the collapse is slowed down, and this enhances the fragments' change to survive. However, this effect happens up to a threshold density below which single systems tend to form. On the other hand, by setting a bigger initial perturbation amplitude, the collapse is faster and in some cases a final single object is formed.
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arxiv:1103.0752
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We have directly measured quasiparticle number fluctuations in a thin film superconducting Al resonator in thermal equilibrium. The spectrum of these fluctuations provides a measure of both the density and the lifetime of the quasiparticles. We observe that the quasiparticle density decreases exponentially with decreasing temperature, as theoretically predicted, but saturates below 160 mK to 25-55 per cubic micron. We show that this saturation is consistent with the measured saturation in the quasiparticle lifetime, which also explains similar observations in qubit decoherence times.
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arxiv:1103.0758
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We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.
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arxiv:1103.0787
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The problem of privately releasing data is to provide a version of a dataset without revealing sensitive information about the individuals who contribute to the data. The model of differential privacy allows such private release while providing strong guarantees on the output. A basic mechanism achieves differential privacy by adding noise to the frequency counts in the contingency tables (or, a subset of the count data cube) derived from the dataset. However, when the dataset is sparse in its underlying space, as is the case for most multi-attribute relations, then the effect of adding noise is to vastly increase the size of the published data: it implicitly creates a huge number of dummy data points to mask the true data, making it almost impossible to work with. We present techniques to overcome this roadblock and allow efficient private release of sparse data, while maintaining the guarantees of differential privacy. Our approach is to release a compact summary of the noisy data. Generating the noisy data and then summarizing it would still be very costly, so we show how to shortcut this step, and instead directly generate the summary from the input data, without materializing the vast intermediate noisy data. We instantiate this outline for a variety of sampling and filtering methods, and show how to use the resulting summary for approximate, private, query answering. Our experimental study shows that this is an effective, practical solution, with comparable and occasionally improved utility over the costly materialization approach.
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arxiv:1103.0825
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We propose a phenomenological QCD sum rule with an explicit diquark field to investigate the essential ingredients inside the hadrons. Introducing the mass (m_\phi) and the condensate (\phi^2) for the diquark field as parameters in the model, we find that the sum rule works well for Lambda, Lambda_c and Lambda_b. This implies that these Lambda baryons can be represented by a diquark and a quark configuration. We also find that there is a duality relation among the parameters (m_\phi, \phi^2), for which the sum rule is equally good. In the limit when \phi^2 =0 we find m_\phi=0.4 GeV, which can be thought as the constituent diquark mass.
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arxiv:1103.0826
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The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg's uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, have been used in the experimental demonstration of the dynamical Casimir effect, and may soon be able to realize the elusive verification of analogue Hawking radiation. This article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analogue, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.
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arxiv:1103.0835
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We report on microwave measurements on DyBa$_2$Cu$_3$O$_{7-\rm\delta}$ monodomains grown by the top-seeded melt-textured technique. We measured the field increase of the surface resistance $R_{\rm s}(H)$ in the a-b plane at 48.3 GHz. Measurements were performed at fixed temperatures in the range 70 K - $T_{\rm c}$ with a static magnetic field $\mu_0H<0.8$ T parallel to the c-axis. Low field steep increase of the dissipation, typical signature of the presence of weak links, is absent, thus indicating the single-domain behaviour of the sample under study. The magnetic field dependence of $R_{\rm s}(H)$ is ascribed to the dissipation caused by vortex motion. The analysis of $X_{\rm s}(H)$ points to a free-flow regime, thus allowing to obtain the vortex viscosity as a function of temperature. We compare the results with those obtained on RE-BCO systems. In particular, we consider strongly pinned films of YBa$_2$Cu$_3$O$_{7-\rm\delta}$ with nanometric BaZrO$_3$ inclusions.
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arxiv:1103.0858
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Recent work shows that a quantum spin liquid can arise in realistic fermionic models on a honeycomb lattice. We study the quantum spin-1/2 Heisenberg honeycomb model, considering couplings J1, J2, and J3 up to third nearest neighbors. We use an unbiased pseudofermion functional renormalization group method to compute the magnetic susceptibility and determine the ordered and disordered states of the model. Aside from antiferromagnetic, collinear, and spiral order domains, we find a large paramagnetic region at intermediate J2 coupling. For larger J2 within this domain, we find a strong tendency to staggered dimer ordering, while the remaining paramagnetic regime for low J2 shows only weak plaquet and staggered dimer response. We suggest this regime to be a promising region to look for quantum spin liquid states when charge fluctuations would be included.
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arxiv:1103.0859
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We suggest a realization of a bistable non-volatile memory capacitor (memcapacitor). Its design utilizes a strained elastic membrane as a plate of a parallel-plate capacitor. The applied stress generates low and high capacitance configurations of the system. We demonstrate that a voltage pulse of an appropriate amplitude can be used to reliably switch the memcapacitor into the desired capacitance state. Moreover, charged-voltage and capacitance-voltage curves of such a system demonstrate hysteresis and transition into a chaotic regime in a certain range of ac voltage amplitudes and frequencies. Membrane memcapacitor connected to a voltage source comprises a single element nonautonomous chaotic circuit.
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arxiv:1103.0910
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We report Brownian dynamics (BD) simulation and theoretical results for a system of spherical colloidal particles with permanent dipole moments in a rotating magnetic field. Performing simulations at a fixed packing fraction and dipole coupling parameter, we construct a full non-equilibrium phase diagram as function of the driving frequency ($\omega_0$) and field strength ($B_0$). This diagram contains both synchronized states, where the individual particles follow the field with (on average) constant phase difference, and asynchronous states. The synchronization is accompanied by layer formation, i.e. by spatial symmetry-breaking, similar to systems of induced dipoles in rotating fields. In the permanent-dipole case, however, too large $\omega_0$ yield a breakdown of layering, supplemented by complex changes of the single-particle rotational dynamics from synchronous to asynchronous behavior. We show that the limit frequencies $\omega_c$ can be well described as a bifurcation in the nonlinear equation of motion of a single particle rotating in a viscous medium. Finally, we present a simple density functional theory, which describes the emergence of layers in perfectly synchronized states as an equilibrium phase transition.
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arxiv:1103.0925
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Relativistic Brownian motion can be inexpensively demonstrated on a graphene chip. The interplay of stochastic and relativistic dynamics, governing the transport of charge carrier in graphene, induces noise-controlled effects such as (i) a stochastic effective mass, detectable as a suppression of the particle mobility with increasing the temperature; (ii) a transverse ratchet effect, measurable as a net current orthogonal to an ac drive on an asymmetric substrate, and (iii) a chaotic stochastic resonance. Such properties can be of practical applications in the emerging graphene technology.
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arxiv:1103.0945
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We consider a mirror symmetry of simple elliptic singularities. In particular, we construct isomorphisms of Frobenius manifolds among the one from the Gromov--Witten theory of a weighted projective line, the one from the theory of primitive forms for a universal unfolding of a simple elliptic singularity and the one from the invariant theory for an elliptic Weyl group. As a consequence, we give a geometric interpretation of the Fourier coefficients of an eta product considered by K. Saito.
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arxiv:1103.0951
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Recent optical measurements of deeply underdoped cuprates have revealed that a coherent Drude response persists well below the end of the superconducting dome. In addition, no large increase in optical effective mass has been observed, even at dopings as low as 1%. We show that this behavior is consistent with the resonating valence bond spin-liquid model proposed by Yang, Rice, and Zhang. In this model, the overall reduction in optical conductivity in the approach to the Mott insulating state is caused not by an increase in effective mass, but by a Gutzwiller factor, which describes decreased coherence due to correlations, and by a shrinking of the Fermi surface, which decreases the number of available charge carriers. We also show that in this model, the pseudogap does not modify the low-temperature, low-frequency behavior, though the magnitude of the conductivity is greatly reduced by the Gutzwiller factor. Similarly, the profile of the temperature dependence of the microwave conductivity is largely unchanged in shape, but the Gutzwiller factor is essential in understanding the observed difference in magnitude between ortho-I and -II YBa$_2$Cu$_3$O$_y$.
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arxiv:1103.0970
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If $\Omega$ is a bounded domain in $\mathbb R^N$, we study conditions on a Radon measure $\mu$ on $\partial\Omega$ for solving the equation $-\Delta u+e^{u}-1=0$ in $\Omega$ with $u=\mu$ on $\partial\Omega$. The conditions are expressed in terms of nonlinear capacities.
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arxiv:1103.0975
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Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term. Using this equivalence and a 3+1 decomposition of the theory it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (hamiltonian and momentum) constraints. In this paper we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames, is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.
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arxiv:1103.0984
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Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a {\it sufficient enlargement} for $X$ if, for an arbitrary isometric embedding of $X$ into a Banach space $Y$, there exists a linear projection $P:Y\to X$ such that $P(B_Y)\subset A$. Each finite dimensional normed space has a minimal-volume sufficient enlargement which is a parallelepiped, some spaces have "exotic" minimal-volume sufficient enlargements. The main result of the paper is a characterization of spaces having "exotic" minimal-volume sufficient enlargements in terms of Auerbach bases.
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arxiv:1103.0997
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Oxides containing iridium ions display a range of magnetic and conducting properties that depend on the delicate balance between interactions and are controlled, at least in part, by the details of the crystal architecture. We have used muon-spin rotation ($\mu$SR) to study the local field in four iridium oxides, Ca$_4$IrO$_6$, Ca$_5$Ir$_3$O$_{12}$, Sr$_3$Ir$_2$O$_7$ and Sr$_2$IrO$_4$, which show contrasting behavior. Our $\mu$SR data on Ca$_4$IrO$_6$ and Ca$_5$Ir$_3$O$_{12}$ are consistent with conventional antiferromagnetism where quasistatic magnetic order develops below $T_{\rm N}=13.85(6)$ K and 7.84(7) K respectively. A lower internal field is observed for Ca$_5$Ir$_3$O$_{12}$, as compared to Ca$_4$IrO$_6$ reflecting the presence of both Ir$^{4+}$ and Ir$^{5+}$ ions, resulting in a more magnetically dilute structure. Muon precession is only observed over a restricted range of temperature in Sr$_3$Ir$_2$O$_7$, while the Mott insulator Sr$_2$IrO$_4$ displays more complex behavior, with the $\mu$SR signal containing a single, well-resolved precession signal below $T_{\rm N}=230$\,K, which splits into two precession signals at low temperature following a reorientation of the spins in the ordered state.
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arxiv:1103.1036
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Conformal mechanics related to the near horizon extreme Kerr-Newman-AdS-dS black hole is studied. A unique N=2 supersymmetric extension of the conformal mechanics is constructed.
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arxiv:1103.1047
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We examine the validity of the generalized second law of thermodynamics in a non-flat universe in the presence of viscous dark energy. At first we assume that the universe filled only with viscous dark energy. Then, we extend our study to the case where there is an interaction between viscous dark energy and pressureless dark matter. We examine the time evolution of the total entropy, including the entropy associated with the apparent horizon and the entropy of the viscous dark energy inside the apparent horizon. Our study show that the generalized second law of thermodynamics is always protected in a universe filled with interacting viscous dark energy and dark matter in a region enclosed by the apparent horizon. Finally, we show that the the generalized second law of thermodynamics is fulfilled for a universe filled with interacting viscous dark energy and dark matter in the sense that we take into account the Casimir effect.
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arxiv:1103.1067
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We consider scattering of a plane electromagnetic wave by a wormhole. It is found that the scattered wave is partially depolarized and has a specific interference picture depending on parameters of the wormhole and the distance to the observer. It is proposed that such features can be important in the direct search of wormholes.
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arxiv:1103.1113
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Spiral galaxies are surrounded by a widely distributed hot coronal gas and seem to be fed by infalling clouds of neutral hydrogen gas with low metallicity and high velocities. We numerically study plasma waves produced by the collisions of these high-velocity clouds (HVCs) with the hot halo gas and with the gaseous disk. In particular, we tackle two problems numerically: 1) collisions of HVCs with the galactic halo gas and 2) the dispersion relations to obtain the phase and group velocities of plasma waves from the equations of plasma motion as well as further important physical characteristics such as magnetic tension force, gas pressure, etc. The obtained results allow us to understand the nature of MHD waves produced during the collisions in galactic media and lead to the suggestion that these waves can heat the ambient halo gas. These calculations are aiming at leading to a better understanding of dynamics and interaction of HVCs with the galactic halo and of the importance of MHD waves as a heating process of the halo gas.
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arxiv:1103.1114
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Trumpler 16 is a well--known rich star cluster containing the eruptive supergiant $\eta$ Carin\ae\ and located in the Carina star-forming complex. In the context of the Chandra Carina Complex Project, we study Trumpler 16 using new and archival X-ray data. A revised X-ray source list of the Trumpler 16 region contains 1232 X-ray sources including 1187 likely Carina members. These are matched to 1047 near-infrared counterparts detected by the HAWK-I instrument at the VLT allowing for better selection of cluster members. The cluster is irregular in shape. Although it is roughly circular, there is a high degree of sub-clustering, no noticeable central concentration and an extension to the southeast. The high--mass stars show neither evidence of mass segregation nor evidence of strong differential extinction. The derived power-law slope of the X-ray luminosity function for Trumpler 16 reveals a much steeper function than the Orion Nebula Cluster implying different ratio of solar- to higher-mass stars. We estimate the total Trumpler 16 pre-main sequence population to be > 6500 Class II and Class III X-ray sources. An overall K-excess disk frequency of ~ 8.9% is derived using the X-ray selected sample, although there is some variation among the sub-clusters, especially in the Southeastern extension. X-ray emission is detected from 29 high--mass stars with spectral types between B2 and O3.
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arxiv:1103.1126
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In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to prove the existence of solitons in some dynamical systems.
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arxiv:1103.1131
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We introduce the notion of a manifold admitting a simple compact Cartan 3-form $\om^3$. We study algebraic types of such manifolds specializing on those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form $\om^3$. We prove the existence of an algebra of multi-symplectic forms $\phi^l$ on these manifolds. Cohomology groups associated with complexes of differential forms on $M^n$ in presence of such a closed multi-symplectic form $\phi^l$ and their relations with the de Rham cohomologies of $M$ are investigated. We show rigidity of a class of strongly associative (resp. strongly coassociative) submanifolds. We include an appendix describing all connected simply connected complete Riemannian manifolds admitting a parallel 3-form.
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arxiv:1103.1201
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We derive here a robust bound on the effective number of neutrinos from constraints on primordial nucleosynthesis yields of deuterium and helium. In particular, our results are based on very weak assumptions on the astrophysical determination of the helium abundance, namely that the minimum effect of stellar processing is to keep constant (rather than increase, as expected) the helium content of a low-metallicity gas. Using the results of a recent analysis of extragalactic HII regions as upper limit, we find that Delta Neff<= 1 at 95 % C.L., quite independently of measurements on the baryon density from cosmic microwave background anisotropy data and of the neutron lifetime input. In our approach, we also find that primordial nucleosynthesis alone has no significant preference for an effective number of neutrinos larger than the standard value. The ~2 sigma hint sometimes reported in the literature is thus driven by CMB data alone and/or is the result of a questionable regression protocol to infer a measurement of primordial helium abundance.
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arxiv:1103.1261
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Recent experiments on thin-film microcavities give evidence of Bose condensation of exciton-polariton states. Inspired by these observations, we consider the possibility that such exotic "half-light/half matter" states could be observed in thin-film organic semiconductors where the oscillator strength is generally stronger than in inorganic systems. Here we present a theoretical model and simulations of macroscopic exciton-polartiton condensates in thracene thin films sandwiched within a micro-meter scale resonant cavity and establish criteria for the conditions under which BEC could be achieved in these systems. We consider the effect of lattice disorder on the threshold intensities necessary to create polartion superfluid states and conclude that even allowing for up to 5% angular disorder of the molecules within the crystal lattice, the superfluid transition remains sharp.
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arxiv:1103.1326
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Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications from high temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers due to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we employ a degenerate Bose gas confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary an applied field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase the interaction between the spins is overwhelmed by the applied field which aligns the spins. In the antiferromagnetic phase the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in-situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, improving our understanding of real magnetic materials.
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arxiv:1103.1372
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Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunctions of quantum graph. The theorem stipulates that, after ordering the eigenvalues as a non decreasing sequence, the number of nodal domains $\nu_n$ of the $n$-th eigenfunction satisfies $n\ge \nu_n$. Here, we provide a new interpretation for the Courant nodal deficiency $d_n = n-\nu_n$ in the case of quantum graphs. It equals the Morse index --- at a critical point --- of an energy functional on a suitably defined space of graph partitions. Thus, the nodal deficiency assumes a previously unknown and profound meaning --- it is the number of unstable directions in the vicinity of the critical point corresponding to the $n$-th eigenfunction. To demonstrate this connection, the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail.
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arxiv:1103.1423
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We report clear observations of the magnetic Meissner effect in arrays of superconducting 4 {\AA} carbon nanotubes grown in the linear channels of AlPO4-5 (AFI) zeolite single crystals. Both bulk magnetization and magnetic torque experiments show a clear signature of the lower critical Hc1 transition, a pronounced difference in zero-field cooled and field cooled branches during temperature sweeps below 6K, and signatures of 1D superconducting fluctuations below ~15-18 K. These experiments extend the magnetic phase diagram we obtained previously by resistive experiments [Z. Wang et al., Phys. Rev. B 81, 174530 (2010)] towards low magnetic fields and within the range of zero resistance.
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arxiv:1103.1459
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The polarized antiquark distributions in the proton can be measured by studying spin asymmetries in vector boson production in longitudinally polarized proton-proton collisions. The STAR and PHENIX experiments at BNL RHIC have reported first observations of single spin asymmetries in $W^\pm$-production most recently. We compute the QCD corrections to single and double spin asymmetries, taking account of the leptonic decay of the $W^\pm$ boson and of restrictions on the kinematical acceptance of the detectors. The QCD corrections have only a small impact on the asymmetries, such that a reliable extraction of the polarized antiquark distributions can be envisaged once more precise measurements are made.
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arxiv:1103.1465
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Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumptions that guarantee the consistency of discrete-time g-estimation. In more general cases, when those assumptions are violated, we propose a controlling-the-future method that performs at least as well as g-estimation in most scenarios and which provides consistent estimation in some cases where g-estimation is severely inconsistent. We apply the methods discussed in this paper to simulated data, as well as to a data set collected following a massive flood in Bangladesh, estimating the effect of diarrhea on children's height. Results from different methods are compared in both simulation and the real application.
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arxiv:1103.1472
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We reconsider the theory of scattering for the Wave-Schr\"odinger system and more precisely the local Cauchy problem with infinite initial time, which is the main step in the construction of the wave operators. Using a method due to Nakanishi, we eliminate a loss of regularity between the Schr\"odinger asymptotic data and the Schr\"odinger solution in the treatment of that problem, in the special case of vanishing asymptotic data for the wave field.
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arxiv:1103.1538
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Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f-electron valence fluctuations. Our calculations introduce "symplectic Hubbard operators": an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-coherent mixing of the empty and doubly occupied configurations of the mixed valent ion. This effect redistributes the f-electron charge within the unit cell. Our theory predicts a sharp superconducting shift in the nuclear quadrupole resonance frequency associated with this redistribution. We calculate the magnitude and sign of the predicted shift expected in CeCoIn_5.
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arxiv:1103.1550
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Recently a quantum group deformation of EPRL spinfoam model was proposed in arXiv:1012.4216 by one of the authors, and in arXiv:1012.4784 by Fairbairn and Meusburger. It is interesting to study the high spin asymptotics of the quantum group spinfoam model, to see if it gives the discrete Einstein gravity with cosmological constant as its semiclassical limit. In this article we propose a new technique, which can simplify the analysis of the high spin asymptotics for quantum group spinfoam vertex amplitude. This technique can generalize the spinfoam asymptotic analysis developed by Barrett, et al to quantum group spinfoam. As a preparation of asymptotic analysis, we define and analyze the coherent states and coherent intertwiners for quantum group, which has certain "factorization properties". We show that in the high spin limit of quantum group spinfoam, many q-deformed noncommutative ingredients become classical and commutative. In particular, the squared norm of coherent intertwiner and the (Euclidean) vertex amplitude become integrals on classical group, while there are some additional terms (written in terms of classical group variables) make quantum group corrections to the usual (classical group) coherent intertwiner and vertex amplitude. These quantum group correction terms turn out to be proportional to the deformation parameter, which hopefully gives the cosmological term as its semiclassical limit.
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arxiv:1103.1597
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Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations relating the one-particle Green's function to its functional derivative with respect to an external perturbing potential. In the present work we apply a linear response expansion in order to obtain insights in various approximations for Green's functions calculations. The expansion leads to an effective screening, while keeping the effects of the interaction to all orders. In order to study various aspects of the resulting equations we discretize them, and retain only one point in space, spin, and time for all variables. Within this one-point model we obtain an explicit solution for the Green's function, which allows us to explore the structure of the general family of solutions, and to determine the specific solution that corresponds to the physical one. Moreover we analyze the performances of established approaches like $GW$ over the whole range of interaction strength, and we explore alternative approximations. Finally we link certain approximations for the exact solution to the corresponding manipulations for the differential equation which produce them. This link is crucial in view of a generalization of our findings to the real (multidimensional functional) case where only the differential equation is known.
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arxiv:1103.1630
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Context: Understanding the evolution of the dark matter halos of galaxies after they become part of a cluster is essential for understanding the evolution of these satellite galaxies. Aims: We investigate the potential of galaxy-galaxy lensing to map the halo density profiles of galaxies in clusters. Methods: We propose a method that separates the weak-lensing signal of the dark-matter halos of galaxies in clusters from the weak-lensing signal of the cluster's main halo. Using toy cluster models as well as ray-tracing through N-body simulations of structure formation along with semi-analytic galaxy formation models, we test the method and assess its performance. Results: We show that with the proposed method, one can recover the density profiles of the cluster galaxy halos in the range 30 - 300 kpc. Using the method, we find that weak-lensing signal of cluster member galaxies in the Millennium Simulation is well described by an Navarro-Frenk-White (NFW) profile. In contrast, non-singular isothermal mass distribution (like PIEMD) model provide a poor fit. Furthermore, we do not find evidence for a sharp truncation of the galaxy halos in the range probed by our method. Instead, there is an observed overall decrease of the halo mass profile of cluster member galaxies with increasing time spent in the cluster. This trend, as well as the presence or absence of a truncation radius, should be detectable in future weak-lensing surveys like the Dark Energy Survey (DES) or the Large Synoptic Survey Telescope (LSST) survey. Such surveys should also allow one to infer the mass-luminosity relation of cluster galaxies with our method over two decades in mass. Conclusions: It is possible to recover in a non-parametric way the mass profile of satellite galaxies and their dark matter halos in future surveys, using our proposed weak lensing method.
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arxiv:1103.1635
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The null horizon focusing equation is equivalent via the fluid/gravity correspondence to the entropy balance law of the fluid. Using this equation we derive a simple novel formula for the bulk viscosity of the fluid. The formula is expressed in terms of the dependence of scalar fields at the horizon on thermodynamic variables such as the entropy and charge densities. We apply the formula to three classes of gauge theory plasmas: non-conformal branes, perturbations of the N=4 supersymmetric Yang-Mills theory and holographic models of QCD, and discuss its range of applicability.
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arxiv:1103.1657
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We introduce a renormalized 1PI vertex part scalar field theory setting in momentum space to computing the critical exponents $\nu$ and $\eta$, at least at two-loop order, for a layered parallel plate geometry separated by a distance L, with periodic as well as antiperiodic boundary conditions on the plates. We utilize massive and massless fields in order to extract the exponents in independent ultraviolet and infrared scaling analysis, respectively, which are required in a complete description of the scaling regions for finite size systems. We prove that fixed points and other critical amounts either in the ultraviolet or in the infrared regime dependent on the plates boundary condition are a general feature of normalization conditions. We introduce a new description of typical crossover regimes occurring in finite size systems. Avoiding these crossovers, the three regions of finite size scaling present for each of these boundary conditions are shown to be indistinguishable in the results of the exponents in periodic and antiperiodic conditions, which coincide with those from the (bulk) infinite system.
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arxiv:1103.1661
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We report the detection of a strong, reversing magnetic field and variable H-alpha emission in the bright helium-weak star HD 176582 (HR 7185). Spectrum, magnetic and photometric variability of the star are all consistent with a precisely determined period of 1.5819840 +/- 0.0000030 days which we assume to be the rotation period of the star. From the magnetic field curve, and assuming a simple dipolar field geometry, we derive a polar field strength of approximately 7 kG and a lower limit of 52 degrees for the inclination of the rotation axis. However, based on the behaviour of the H-alpha emission we adopt a large inclination angle of 85 degrees and this leads to a large magnetic obliquity of 77 degrees. The H-alpha emission arises from two distinct regions located at the intersections of the magnetic and rotation equators and which corotate with the star at a distance of about 3.5 R* above its surface. We estimate that the emitting regions have radial and meridional sizes on the order of 2 R* and azimuthal extents (perpendicular to the magnetic equator) of less than approximately 0.6 R*. HD 176582 therefore appears to show many of the cool magnetospheric phenomena as that displayed by other magnetic helium-weak and helium-strong stars such as the prototypical helium-strong star sigma Ori E. The observations are consistent with current models of magnetically confined winds and rigidly-rotating magnetospheres for magnetic Bp stars.
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arxiv:1103.1685
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Many new physics models predict the existence of TeV-scale charged gauge boson $W^\prime$ together with Higgs boson(s). We study the $W^\prime WH$ interaction and explore the angular distribution of charged lepton to distinguish $W_R^\prime WH$ from $W_L^\prime WH$ in $pp\to HW\to b \bar b l \nu$ process at the LHC. It is found that a new type forward-backward asymmetry($A_{FB}$) relating to the angle between the direction of the charged lepton in $W$ rest frame and that of the reconstructed $W^\prime$ in laboratory frame is useful to investigate the properties of $W^\prime W H$ interaction. We analyze the Standard Model backgrounds and develop a set of cuts to highlight the signal and suppress the backgrounds at LHC. We find that $A_{FB}$ can reach 0.03(-0.07) for $W_R^\prime$($W_L^\prime$) production at $\sqrt{S}=14$ TeV.
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arxiv:1103.1688
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We present the results of C18O(J=1-0) mapping observations of a 20'x18' area in the Lynds 1204 molecular cloud associated with the Sharpless 2-140 (S140) H II region. The C18O cube (alpha-delta-vLSR) data shows that there are three clumps with sizes of \sim 1 pc in the region. Two of them have peculiar red shifted velocity components at their edges, which can be interpreted as the results of the interaction between the cloud and the Cepheus Bubble. From the C18O cube data, the clumpfind identified 123 C18O cores, which have mean radius, velocity width in FWHM, and LTE mass of 0.36\pm0.07 pc, 0.37\pm0.09 km s-1, and 41\pm29 Msun, respectively. All the cores in S140 are most likely to be gravitationally bound by considering the uncertainty in the C18O abundance. We derived a C18O core mass function (CMF), which shows a power-law-like behavior above a turnover at 30 Msun. The best-fit power-law index of -2.1\pm0.2 is quite consistent with those of the IMF and the C18O CMF in the OMC-1 region by Ikeda & Kitamura (2009). Kramer et al. (1998) estimated the power-law index of -1.65 in S140 from the C18O(J=2-1) data, which is inconsistent with this study. However, the C18O(J=2-1) data are spatially limited to the central part of the cloud and are likely to be biased toward high-mass cores, leading to the flatter CMF. Consequently, this study and our previous one strongly support that the power-law form of the IMF has been already determined at the density of \sim 10^{3-4} cm^{-3}, traced by the C18O(J=1-0) line.
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arxiv:1103.1712
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One of the hallmarks of biological organisms is their ability to integrate disparate information sources to optimize their behavior in complex environments. How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since organismal functional complexity is not well-defined. We present here several candidate measures that quantify information and integration, and study their dependence on fitness as an artificial agent ("animat") evolves over thousands of generations to solve a navigation task in a simple, simulated environment. We compare the ability of these measures to predict high fitness with more conventional information-theoretic processing measures. As the animat adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent. We suggest that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory. A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the animat, and that such measures can be used to quantify functional complexity even in the absence of fitness data.
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arxiv:1103.1791
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Effects of non-magnetic disorder on the critical temperature T_c and on diamagnetism of quasi-one-dimensional superconductors are reported. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between wires and that T_c vanishes discontinuously at a critical disorder-strength. The parallel and transverse components of the penetration-depth are evaluated. They diverge at different critical temperatures T_c^{(1)} and T_c, which correspond to pair-breaking and phase-coherence breaking respectively. The interplay between disorder and quantum phase fluctuations is shown to result in quantum critical behavior at T=0, which manifests itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.
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arxiv:1103.1806
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In lattice field theory, renormalizable simulation algorithms are attractive, because their scaling behaviour as a function of the lattice spacing is predictable. Algorithms implementing the Langevin equation, for example, are known to be renormalizable if the simulated theory is. In this paper we show that the situation is different in the case of the molecular-dynamics evolution on which the HMC algorithm is based. More precisely, studying the phi^4 theory, we find that the hyperbolic character of the molecular-dynamics equations leads to non-local (and thus non-removable) ultraviolet singularities already at one-loop order of perturbation theory.
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arxiv:1103.1810
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We study the dependence of the Kondo temperature on the gate voltage in a strongly blockaded quantum dot with a small single-particle level spacing. We show that the dependence cannot be fitted to that of the Anderson impurity model with the gate voltage-independent level width. The effect originates in high-order tunneling processes, which make a dominant contribution to the exchange amplitude when the gate voltage is tuned away from the middle of the Coulomb blockade valley.
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arxiv:1103.1837
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We complete the study of the regularity for Trudinger's equation by proving that weak solutions are H\"older continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincar\'e inequality. The proof uses the Harnack inequality and intrinsic scaling.
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arxiv:1103.1845
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When $R$ is a non-archimedean real closed field we say that a function $f\in R(\bar{X})$ is finitary at a point $\bar{b}\in R^n$ if on some neighborhood of $\bar{b}$ the defined values of $f$ are in the finite part of $R$. In this note we give a characterization of rational functions which are finitary on a set defined by positivity and finiteness conditions. The main novel ingredient is a proof that OVF-integrality has a natural topological definition, which allows us to apply a known Ganzstellensatz for the relevant valuation. We also give some information about the Kochen geometry associated with OVF-integrality.
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arxiv:1103.1873
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A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the proof yields generalizations to directional local linear dependence and evaluations in general algebras over fields of arbitrary characteristic. A main feature of the proof is that it makes it possible to deduce bounds on the size of the matrices where the (directional) local linear dependence needs to be tested in order to establish linear dependence.
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arxiv:1103.1884
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We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the cluster state needed for the computation and its consumption by measurements are carried out simultaneously. As a consequence, effective clusters of one spatial dimension fewer than in the standard approach are sufficient for computation. In particular, universal computation requires only a one-dimensional array of memories. The scheme applies to discrete-variable systems of any dimension as well as to continuous-variable ones, and both are treated equivalently under the light of local complementation of graphs. In this way our formalism introduces a general framework that encompasses and generalizes in a unified manner some previous system-dependent proposals. The procedure is intrinsically well-suited for implementations with atom-photon interfaces.
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arxiv:1103.1907
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The experimental realization of quantum degenerate cold Fermi gases with large hyperfine spins opens up a new opportunity for exotic many-body physics.
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arxiv:1103.1933
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By an electrical-pump--optical-probe technique we show that the electric-field-induced reversal of the magnetic order parameter in multiferroic MnWO$_4$ occurs on the time scale of milliseconds and maintains a rigid coupling of the magnetization to the magnetically induced electric polarization. The temporal progression of the spatially resolved domain structure was imaged with nanosecond resolution by optical second harmonic generation and compared to the quasi-static domain reversal. A qualitative model gives an estimate of why the magnetoelectric order-parameter reversal in the magnetically induced ferroelectrics is not inherently ultrafast.
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arxiv:1103.2066
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In this lecture, we present some results on Gaussian (or Rademacher) random series of trace class operators, mainly due jointly with F. Lust-Piquard. We will emphasize the probabilistic reformulation of these results, as well as the open problems suggested by them. We start by a brief survey of what is known about the problem of characterizing a.s. convergent (Gaussian or Rademacher) series of random vectors in a Banach space. The main result presented here is that for certain pairs of Banach spaces $E,F$ that include Hilbert spaces (and type 2 spaces with the analytic UMD property), we have $$ R(E\hat\otimes F) =R(E)\hat\otimes F + E\hat\otimes R(F) $$ where $R(E)$ denotes the space of convergent Rademacher series with coefficients in $E$ and $E\hat\otimes F$ denotes the projective tensor product.
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arxiv:1103.2090
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Photoproduction of neutral pseudoscalar mesons $\pi^0,\eta(547)$ and $\eta'(958)$ in the Coulomb field of an atomic nucleus is studied using a model which describes the Primakoff and nuclear parts of the production amplitude. At high energies the nuclear background is dominated by the exchange of $C$-parity odd Regge trajectories. In the coherent production the isospin filtering makes the $\omega(782)$ a dominant trajectory. The calculations are in agreement with $\pi^0$ data from JLAB provided the photon shadowing and final state interactions of mesons are taken into account. The kinematic conditions which allow to study the Primakoff effect in $\eta$ and $\eta'$ photoproduction off nuclei are further discussed. We also give predictions for the higher energies available at the JLAB upgrade.
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arxiv:1103.2097
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We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal. 34 (1997), 2028--2042] it is based on the optimization algorithm threshold accepting. Our improvements include, amongst others, a non-uniform sampling strategy which is more suited for higher-dimensional inputs, and rounding steps which transform axis-parallel boxes, on which the discrepancy is to be tested, into \emph{critical test boxes}. These critical test boxes provably yield higher discrepancy values, and contain the box that exhibits the maximum value of the local discrepancy. We provide comprehensive experiments to test the new algorithm. Our randomized algorithm computes the exact discrepancy frequently in all cases where this can be checked (i.e., where the exact discrepancy of the point set can be computed in feasible time). Most importantly, in higher dimension the new method behaves clearly better than all previously known methods.
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arxiv:1103.2102
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The electroweak (EW) symmetry breaking in the simplest supersymmetric (SUSY) extensions of the standard model (SM), i.e. minimal and next-to-minimal supersymmetric standard models (MSSM and NMSSM), is considered. The spectrum of the Higgs particles, upper bound on the mass of the lightest Higgs boson and little hierarchy problem are discussed. The breakdown of gauge symmetry and Higgs phenomenology within the E6 inspired SUSY models with extra U(1)' factor are briefly reviewed.
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arxiv:1103.2141
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The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are demonstrated. A model based on small deflection thin shell theory, the equations of which are solved in conjunction with variational principles, is presented. In the exact formulation, axisymmetric and inextensional assumptions are not used initially and the elastic medium is modelled as a Winkler foundation, i.e., using uncoupled radial springs with a constant foundation modulus that is independent of wave numbers of shell buckling modes. Simplified approximations based on a Rayleigh-Ritz approach are also introduced for critical buckling pressure and mode number with a considerable degree of accuracy. Characteristic modal shapes are demonstrated for a wide range of material and geometric parameters. A phase diagram is established to obtain the requisite thickness to radius, and stiffness ratios for a desired mode profile. The present exact formulation can be readily extended to apply to more general cases of non-axisymmetric buckling problems.
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arxiv:1103.2179
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It is generally believed that in a superconducor Cooper pairs are broken at above-critical current region, corresponding to the lost of superconductivity. We suggest that, under some circumstance, Cooper pairs could still exist above critical current, and that dissipation of the system is caused by the scattering of these pairs. The existence of Cooper pairs in this region can be revealed by investigating the temperature dependence of the electrical resistance.
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arxiv:1103.2211
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We make a comprehensive study of (rigid) N=1 supersymmetric sigma-models with general K\"ahler potentials K and superpotentials w on four-dimensional space-times with boundaries. We determine the minimal (non-supersymmetric) boundary terms one must add to the standard bulk action to make it off-shell invariant under half the supersymmetries without imposing any boundary conditions. Susy boundary conditions do arise from the variational principle when studying the dynamics. Upon including an additional boundary action that depends on an arbitrary real boundary potential B one can generate very general susy boundary conditions. We show that for any set of susy boundary conditions that define a Lagrangian submanifold of the K\"ahler manifold, an appropriate boundary potential B can be found. Thus the non-linear sigma-model on a manifold with boundary is characterised by the tripel (K,B,w). We also discuss the susy coupling to new boundary superfields and generalize our results to supersymmetric junctions between completely different susy sigma-models, living on adjacent domains and interacting through a "permeable" wall. We obtain the supersymmetric matching conditions that allow us to couple models with different K\"ahler potentials and superpotentials on each side of the wall.
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arxiv:1103.2280
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We consider distributed algorithms for data aggregation and function computation in sensor networks. The algorithms perform pairwise computations along edges of an underlying communication graph. A token is associated with each sensor node, which acts as a transmission permit. Nodes with active tokens have transmission permits; they generate messages at a constant rate and send each message to a randomly selected neighbor. By using different strategies to control the transmission permits we can obtain tradeoffs between message and time complexity. Gossip corresponds to the case when all nodes have permits all the time. We study algorithms where permits are revoked after transmission and restored upon reception. Examples of such algorithms include Simple-Random Walk(SRW), Coalescent-Random-Walk(CRW) and Controlled Flooding(CFLD) and their hybrid variants. SRW has a single node permit, which is passed on in the network. CRW, initially initially has a permit for each node but these permits are revoked gradually. The final result for SRW and CRW resides at a single(or few) random node(s) making a direct comparison with GOSSIP difficult. A hybrid two-phase algorithm switching from CRW to CFLD at a suitable pre-determined time can be employed to achieve consensus. We show that such hybrid variants achieve significant gains in both message and time complexity. The per-node message complexity for n-node graphs, such as 2D mesh, torii, and Random geometric graphs, scales as $O(polylog(n))$ and the corresponding time complexity scales as O(n). The reduced per-node message complexity leads to reduced energy utilization in sensor networks.
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arxiv:1103.2289
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NOON states (states of the form $|N>_{a}|0>_{b}+|0>_{a}|N>_{b}$ where $a$ and $b$ are single particle states) have been used for predicting violations of local realism (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state Bose-Einstein condensates as sources in a modified Mach-Zehnder interferometer can lead to the creation of the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$ is a subset of the total number of particles in the two condensates. The modification of the interferometer involves making {}"side" measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter if the phase states are orthogonal. When they are not orthogonal, a {}"feedforward" correction circuit is shown to convert them into proper form so a NOON results. We apply the NOON to the measurement of phase. Here the NOON experiment is equivalent to one in which a large molecule passes through two slits. The NOON components can be recombined in a final beam splitter to show interference.
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arxiv:1103.2304
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Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number $\mathfrak b$. We analyze some of the basic behavior of these properties, showing for instance that the property corresponding to the splitting number $\mathfrak s$ coincides with smoothness. We then settle many of the implication relationships between the properties; these relationships turn out to be closely related to (but not the same as) the Borel Tukey ordering on cardinal characteristics.
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arxiv:1103.2312
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The Kustin-Miller complex construction, due to A. Kustin and M. Miller, can be applied to a pair of resolutions of Gorenstein rings with certain properties to obtain a new Gorenstein ring and a resolution of it. It gives a tool to construct and analyze Gorenstein rings of high codimension. We describe the Kustin-Miller complex and its implementation in the Macaulay2 package KustinMiller, and explain how it can be applied to explicit examples.
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arxiv:1103.2314
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We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural way in algebraic and geometric terms.
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arxiv:1103.2321
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We investigate the distinct properties of two types of flares: eruptive flares associated with CMEs and confined flares without CMEs. Our sample of study includes nine M and X-class flares, all from the same active region (AR), six of which are confined and three others are eruptive. The confined flares tend to be more impulsive in the soft X-ray time profiles and show more slender shapes in the EIT 195 A images, while the eruptive ones are of long-duration events and show much more extended brightening regions. The location of the confined flares are closer to the center of the AR, while the eruptive flares are at the outskirts. This difference is quantified by the displacement parameter, the distance between the AR center and the flare location: the average displacement of the six confined flares is 16 Mm, while that of eruptive ones is as large as 39 Mm. Further, through nonlinear force-free field extrapolation, we find that the decay index of the transverse magnetic field in the low corona (~10 Mm) have a larger value for eruptive flares than that for confined one. In addition, the strength of the transverse magnetic field over the eruptive flare sites is weaker than that over the confined ones. These results demonstrate that the strength and the decay index of background magnetic field may determine whether or not a flare be eruptive or confined. The implication of these results on CME models is discussed in the context of torus instability of flux rope.
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arxiv:1103.2323
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In this talk we introduce the main features of a QCD-based model in which the coupling $\alpha_{s}$ is constrained by an infrared mass scale. We show recent applications of this model to hadron-hadron collisions, gap survival probability calculations, and soft gluon resummation techniques. These results indicate a smooth transition from non-perturbative to perturbative behaviour of the QCD.
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arxiv:1103.2334
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A $Roman\ domination\ function$ on a graph $G=(V, E)$ is a function $f:V(G)\rightarrow\{0,1,2\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The $weight$ of a Roman domination function $f$ is the value $f(V(G))=\sum_{u\in V(G)}f(u)$. The minimum weight of a Roman dominating function on a graph $G$ is called the $Roman\ domination\ number$ of $G$, denoted by $\gamma_{R}(G)$. In this paper, we study the {\it Roman domination number} of generalized Petersen graphs P(n,2) and prove that $\gamma_R(P(n,2)) = \lceil {\frac{8n}{7}}\rceil (n \geq 5)$.
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arxiv:1103.2419
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We show that as the result of the nesting property of the Fermi surface, the quarter-doped Hubbard model on honeycomb lattice is unstable with respect to the formation of a magnetic insulating state with nonzero spin chirality for infinitesimally small strength of electron correlation. The insulating state is found to be topological nontrivial and to have a quantized Hall conductance of $\sigma_{xy}=\frac{e^{2}}{h}$. We find the Fermi surface nesting is robust for arbitrary value of next-nearest-neighbor hopping integral. It is thus very possible that the quarter-doped graphene system will realize such an exotic ground state. We also show that the quarter-doped Hubbard model on honeycomb lattice is in exact equivalence in the weak coupling limit with the 3/4-filled Hubbard model on triangular lattice, in which similar effect is also observed.
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arxiv:1103.2420
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The co-tunneling current through a two-level doubly occupied quantum dot weakly coupled to ferromagnetic leads is calculated in the Coulomb blockade regime. It is shown that the dependence of the differrential conductance on applied voltage has a stair-case structure with different sets of "stairs" for parallel and anti-parallel configurations of magnetization of the leads. Contributions to the current from elastic and inelastic processes are considered distinctly. It is observed that the interference part of the co-tunneling current involves terms corresponding to inelastic processes. Dependence of the co-tunneling current on the phases of the tunneling amplitudes is studied.
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arxiv:1103.2425
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