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We use the harmonic maps ansatz to find exact solutions of the Einstein-Maxwell-Dilaton-Axion (EMDA) equations. The solutions are harmonic maps invariant to the symplectic real group in four dimensions $Sp(4,\Rreal)\sim O(5)$. We find solutions of the EMDA field equations for the one and two dimensional subspaces of the symplectic group. Specially, for illustration of the method, we find space-times that generalise the Schwarzschild solution with dilaton, axion and electromagnetic fields.
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arxiv:0905.4097
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We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e., map-independent) distribution function R(x)=1-e^{-x}(1+x) has been conjectured to exist, for the normalized cycle lengths of the reduced map in the large field limit (J. A. G. Roberts and F. Vivaldi, Nonlinearity 18 (2005) 2171-2192). We show that these statistics correspond to those of a composition of two random involutions, having an appropriate number of fixed points. This model also explains the experimental observation that, asymptotically, almost all cycles are symmetrical, and that the probability of occurrence of repeated periods is governed by a Poisson law.
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arxiv:0905.4135
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In recent years, much work has been devoted to a systematic study of polynomial identities certifying strict or non-strict positivity of a polynomial on a basic closed semialgebraic set. The interest in such identities originates not least from their importance in polynomial optimization. The majority of the important results requires the archimedean condition, which implies that the semialgebraic set has to be compact. This paper introduces the technique of pure states into commutative algebra. We show that this technique allows an approach to most of the recent archimedean Stellensaetze that is considerably easier and more conceptual than the previous proofs. In particular, we reprove and strengthen some of the most important results from the last years. In addition, we establish several such results which are entirely new. They are the first that allow the polynomial to have arbitrary, not necessarily discrete, zeros on the semialgebraic set.
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arxiv:0905.4161
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Masses for the $(Q\bar{s})^{(*)}(\bar{Q}s)^{(*)}$ ($Q=c$ or $b$) molecular states are systematically computed in the framework of QCD sum rules. Technically, contributions of the operators up to dimension six are included in operator product expansion (OPE). The numerical result $4.13\pm0.10 {GeV}$ for $D_{s}^{*}\bar{D}_{s}^{*}$ agrees well with the mass $4143.0\pm2.9\pm1.2 {MeV}$ for Y(4140), which supports the $D_{s}^{*}\bar{D}_{s}^{*}$ molecular configuration for Y(4140).
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arxiv:0905.4178
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In the context of spinfoam models for quantum gravity, we investigate the asymptotical behavior of the 6j-symbol at next-to-leading order. We compute it analytically and check our results against numerical calculations. The 6j-symbol is the building block of the Ponzano-Regge amplitudes for 3d quantum gravity, and the present analysis is directly relevant to deriving the quantum corrections to gravitational correlations in the spinfoam formalism.
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arxiv:0905.4188
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A bi-Hamiltonian hierarchy of quaternion soliton equations is derived from geometric non-stretching flows of curves in the quaternionic projective space $HP^n$. The derivation adapts the method and results in recent work by one of us on the Hamiltonian structure of non-stretching curve flows in Riemannian symmetric spaces $M=G/H$ by viewing $HP^n \simeq {\rm U}(n+1,H)/{\rm U}(1,H) \times {\rm U}(n,H)\simeq {\rm Sp}(n+1)/{\rm Sp}(1)\times {\rm Sp}(n)$ as a symmetric space in terms of compact real symplectic groups and quaternion unitary groups. As main results, scalar-vector (multi-component) versions of the sine-Gordon (SG) equation and the modified Korteveg-de Vries (mKdV) equation are obtained along with their bi-Hamiltonian integrability structure consisting of a shared hierarchy of quaternionic symmetries and conservation laws generated by a hereditary recursion operator. The corresponding geometric curve flows in $HP^n$ are shown to be described by a non-stretching wave map and a mKdV analog of a non-stretching Schrodinger map.
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arxiv:0905.4215
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We argue that it is fundamentally impossible to recover information about quantum superpositions when a system has interacted with a sufficiently large number of degrees of freedom of the environment. This is due to the fact that gravity imposes fundamental limitations on how accurate measurements can be. This leads to the notion of undecidability: there is no way to tell, due to fundamental limitations, if a quantum system evolved unitarily or suffered wavefunction collapse. This in turn provides a solution to the problem of outcomes in quantum measurement by providing a sharp criterion for defining when an event has taken place. We analyze in detail in examples two situations in which in principle one could recover information about quantum coherence: a) "revivals" of coherence in the interaction of a system with the environment and b) the measurement of global observables of the system plus apparatus plus environment. We show in the examples that the fundamental limitations due to gravity and quantum mechanics in measurement prevent both revivals from occurring and the measurement of global observables. It can therefore be argued that the emerging picture provides a complete resolution to the measurement problem in quantum mechanics.
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arxiv:0905.4222
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We analyze the Bombay stock exchange (BSE) price index over the period of last 12 years. Keeping in mind the large fluctuations in last few years, we carefully find out the transient, non-statistical and locally structured variations. For that purpose, we make use of Daubechies wavelet and characterize the fractal behavior of the returns using a recently developed wavelet based fluctuation analysis method. the returns show a fat-tail distribution as also weak non-statistical behavior. We have also carried out continuous wavelet as well as Fourier power spectral analysis to characterize the periodic nature and correlation properties of the time series.
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arxiv:0905.4237
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In the present paper, fixed trace $\beta$-Hermite ensembles generalizing the fixed trace Gaussian Hermite ensemble are considered. For all $\beta$, we prove the Wigner semicircle law for these ensembles by using two different methods: one is the moment equivalence method with the help of the matrix model for general $\beta$, the other is to use asymptotic analysis tools. At the edge of the density, we prove that the edge scaling limit for $\beta$-HE implies the same limit for fixed trace $\beta$-Hermite ensembles. Consequently, explicit limit can be given for fixed trace GOE, GUE and GSE. Furthermore, for even $\beta$, analogous to $\beta$-Hermite ensembles, a multiple integral of the Konstevich type can be obtained.
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arxiv:0905.4255
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We consider the series of the Bergman orthogonal polynomials associated with a bounded simply-connected domain in the complex plane, whose boundary is a Jordan curve. These are the polynomials that are orthonormal with respect to the area measure on the domain. The purpose of this note is to report on recent results regarding the fine asymptotic behaviour of the the leading coefficients and the polynomials in the complement of the domain, in cases when the boundary includes corners. These results complement an investigation started in the 1920's by T. Carleman, who obtained the fine asymptotics for domains with analytic boundaries and carried over by P.K. Suetin in the 1960's, who established them for domains with smooth boundaries.
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arxiv:0905.4256
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The CRESST experiment monitors 300g CaWO_4 crystals as targets for particle interactions in an ultra low background environment. In this paper, we analyze the background spectra that are recorded by three detectors over many weeks of data taking. Understanding these spectra is mandatory if one wants to further reduce the background level, and allows us to cross-check the calibration of the detectors. We identify a variety of sources, such as intrinsic contaminations due to primordial radioisotopes and cosmogenic activation of the target material. In particular, we detect a 3.6keV X-ray line from the decay of 41-Ca with an activity of (26\pm4)\mu Bq, corresponding to a ratio 41-Ca/40-Ca=(2.2\pm0.3)\times10^{-16}.
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arxiv:0905.4282
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We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms min(L) and min(L)+2.
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arxiv:0905.4306
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We introduce a new ideal {\mathfrak D} of the p-adic Galois group-ring associated to a real abelian field and a related ideal {\mathfrak J} for imaginary abelian fields. Both result from an equivariant, Kummer-type pairing applied to Stark units in a Z_p-tower of abelian fields and {\mathfrak J} is linked by explicit reciprocity to a third ideal {\mathfrak S} studied more generally in a previous work. This leads to a new and unifying framework for the Iwasawa Theory of such fields including a real analogue of Stickelberger's Theorem, links with certain Fitting ideals and \Lambda-torsion submodules, and a new exact sequence related to the Main Conjecture.
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arxiv:0905.4336
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We apply the statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet to neutron stars structure. Neutron stars is a classical example where the gravitational field and quantum behavior are combined and produce a macroscopic dense object. Actually, we continue the recent application of Sanudo and Pacheco to white dwarfs structure. We concentrate our study on the connection between complexity and neutron star properties, like maximum mass and the corresponding radius, applying a specific set of realistic equation of states. Moreover, the effect of the strength of the gravitational field on the neutron star structure and consequently on the complexity measure is also investigated. It is seen that neutron stars, consistent with astronomical observations so far, are ordered systems (low complexity), which cannot grow in complexity as their mass increases. This is a result of the interplay of gravity, the short-range nuclear force and the very short-range weak interaction.
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arxiv:0905.4364
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A new approach for the calculation of collisional inverse bremsstrahlung absorption of laser light in dense plasmas is presented. Quantum statistical formalism used allows avoiding {\em ad hoc} cutoffs that were necessary in classical approaches. Thus, the current method remains reliable for strong electron-ion interactions. In addition, both the dynamic, field dependent response and hard electron-ion collisions, are consistently incorporated. The latter were treated in an average manner as a stopping power that in turn was cast into a form of a friction force. Here, for the first time a link between the stopping power and the problem of collisional laser absorption is drawn. This allows the theories developed for the stopping power calculation, such as the quantum T-matrix approach, to be applied to the problem of collisional laser absorption. The new approach accommodates the low- and high-frequency limits explained in the text and is valid for arbitrary laser field intensities. A comparison with classical MD simulation is indicative of the validity of the new method in the wide parameter range tested.
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arxiv:0905.4374
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Let G be a group of type E8 of compact type over the field of rational numbers, let K be a field of characteristic 0, and q the 5-fold Pfister form which is the sum of 32 squares. J-P. Serre posed in a letter to M. Rost written on June 23, 1999 the following problem: Is it true that G is split over K if and only if q is hyperbolic over K? In the present article we construct a cohomological invariant of degree 5 for groups of type E8 with trivial Rost invariant over any field k of characteristic 0, and putting the field of rational numbers for k answer positively this question of Serre. Aside from that, we show that a variety which possesses a special correspondence of Rost is a norm variety.
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arxiv:0905.4384
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We develop a theory of effects of electron-electron collisions on the Dyakonov-Perel' spin relaxation in multi-valley quantum wells. It is shown that the electron-electron scattering rate which governs the spin relaxation is different from that in a single-valley system. The theory is applied to Si/SiGe (001)-grown quantum wells where two valleys are simultaneously populated by free carriers. The dependences of the spin relaxation rate on temperature, electron concentration and valley-orbit splitting are calculated and discussed. We demonstrate that in a wide range of temperatures the electron-electron collisions can govern spin relaxation in high-quality Si/SiGe quantum wells.
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arxiv:0905.4393
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We use the data of Wisconsin H$\alpha$ Mapper (WHAM) to test the hypothesis of whether the amplitudes and spectrum of density fluctuations measured by WHAM can be matched to the data obtained for interstellar scintillations and scattering. To do this, first of all, we adjusted the mean level of signal in the adjacent patches of the data. Then, assuming that the spectrum is Kolmogorov, we successfully matched the amplitudes of turbulence obtained from the WHAM data and the interstellar density fluctuations reported in the existing literature. As a result, we conclude that the existing data is consistent with the Kolmogorov cascade which spans from $10^6$ to $10^{17}$ $m$.
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arxiv:0905.4413
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The asymptotic time derivative of the total dipole signal is proposed as an useful observable to study Isospin equilibration phenomenon in multi-fragmentation processes. The study proceeds through the investigation of the $^{40}Cl+^{28}Si$ system at 40 MeV/nucleon by means of semiclassical microscopic many-body calculations based on the CoMD-II model. In particular, the study has been developed to describe charge/mass equilibration processes involving the gas and liquid "phases" of the total system formed during the early stage of a collision. Through the investigation of dynamical many-body correlations, it is also shown how the proposed observable is rather sensitive to different parameterizations of the isospin dependent interaction.
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arxiv:0905.4419
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Cosmological simulations of Population III star formation suggest an initial mass function (IMF) biased toward very massive stars (M>100Msun) formed in minihalos at redshift z>20, when the cooling is driven by molecular hydrogen. However, this result conflicts with observations of extremely-metal poor (EMP) stars in the Milky Way halo, whose r-process elemental abundances appear to be incompatible with those expected from very massive Population III progenitors. We propose a new solution to the problem in which the IMF of second-generation stars formed at z>10, before reionization, is deficient in sub-solar mass stars, owing to the high cosmic microwave background temperature floor. The observed EMP stars are formed preferentially at z<10 in pockets of gas enriched to metallicity Z>10^{-3.5} Zsun by winds from Population II stars. Our cosmological simulations of dark matter halos like the Milky Way show that current samples of EMP stars can only constrain the IMF of late-time Population III stars, formed at z<13 in halos with virial temperature Tvir~10^4 K. This suggests that pair instability supernovae were not produced primarily by this population. To begin probing the IMF of Population III stars formed at higher redshift will require a large survey, with at least 500 and probably several thousand EMP stars of metallicities Z~10^{-3.5} Zsun.
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arxiv:0905.4505
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We explore the mechanical response of a single polyelectrolyte chain under tension in good and poor solvents using a combination of simulation and theory. In poor solvents, where the equilibrium state of the chain is a collapsed globule, we find that the chain undergoes a globule-coil transition, as the magnitude of the force is increased beyond a critical value. This transition, where the polymer size changes discontinuously from a small to a large value, is accompanied by release of bound counterions from the chain. We explain these results by adhering to a statistical mechanical theory of counter-ion condensation on flexible polyelectrolytes.
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arxiv:0905.4524
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Structural, electrical and magnetic measurements of 115 single crystals of PrIn$_5$ are reported. It has a tetragonal structure and has slightly lower cell volume than its isomorphic counter part CeCoIn_5. The resistivity saturates for T\geq 10K. Analysis of the resistivity for 10K<T< 60K indicates a regular fermi liquid behavior. It does not exhibit superconductivity down to T\sim 1K. The magnetic susceptibility analysis yielded the moment to be 4.00\mu_B indicating that the magnetism of PrCoIn_5 is dominated by Pr^{3+} free ions with some admixture of the magnetic moment of the Co sublattice. The paramagnetic Curie temperature \theta \sim-40K. At low temperatures the susceptibility follows a broad maximum around T_N \sim 14.5K, and increases as the temperature is lowered. The disappearance of superconductivity for T>1K is attributed to chemical pressure effects and magnetic pair breaking.
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arxiv:0905.4536
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For a newform for Gamma_0(N) of even weight k, we prove that its attached p-adic L-function is not identically zero on the group Z_p of the p-adic units. If p >3, we prove that the order of vanishing at any p-adic integer is finite.
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arxiv:0905.4682
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The authors compute the support varieties of all irreducible modules for the small quantum group $u_\zeta(\mathfrak{g})$, where $\mathfrak{g}$ is a simple complex Lie algebra, and $\zeta$ is a primitive $\ell$-th root of unity with $\ell$ larger than the Coxeter number of $\mathfrak{g}$. The calculation employs the prior calculations and techniques of Ostrik and of Nakano--Parshall--Vella, as well as deep results involving the validity of the Lusztig character formula for quantum groups and the positivity of parabolic Kazhdan-Lusztig polynomials for the affine Weyl group. Analogous support variety calculations are provided for the first Frobenius kernel $G_1$ of a reductive algebraic group scheme $G$ defined over the prime field $\mathbb{F}_p$.
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arxiv:0905.4707
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String theory suggests the simultaneous presence of many ultralight axions possibly populating each decade of mass down to the Hubble scale 10^-33eV. Conversely the presence of such a plenitude of axions (an "axiverse") would be evidence for string theory, since it arises due to the topological complexity of the extra-dimensional manifold and is ad hoc in a theory with just the four familiar dimensions. We investigate how upcoming astrophysical experiments will explore the existence of such axions over a vast mass range from 10^-33eV to 10^-10eV. Axions with masses between 10^-33eV to 10^-28eV cause a rotation of the CMB polarization that is constant throughout the sky. The predicted rotation angle is of order \alpha~1/137. Axions in the mass range 10^-28eV to 10^-18eV give rise to multiple steps in the matter power spectrum, that will be probed by upcoming galaxy surveys. Axions in the mass range 10^-22eV to 10^-10eV affect the dynamics and gravitational wave emission of rapidly rotating astrophysical black holes through the Penrose superradiance process. When the axion Compton wavelength is of order of the black hole size, the axions develop "superradiant" atomic bound states around the black hole "nucleus". Their occupation number grows exponentially by extracting rotational energy from the ergosphere, culminating in a rotating Bose-Einstein axion condensate emitting gravitational waves. This mechanism creates mass gaps in the spectrum of rapidly rotating black holes that diagnose the presence of axions. The rapidly rotating black hole in the X-ray binary LMC X-1 implies an upper limit on the decay constant of the QCD axion f_a<2*10^17GeV, much below the Planck mass. This reach can be improved down to the grand unification scale f_a<2*10^16GeV, by observing smaller stellar mass black holes.
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arxiv:0905.4720
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We introduce a randomized algorithm for computing the minimal-norm solution to an underdetermined system of linear equations. Given an arbitrary full-rank m x n matrix A with m<n, any m x 1 vector b, and any positive real number epsilon less than 1, the procedure computes an n x 1 vector x approximating to relative precision epsilon or better the n x 1 vector p of minimal Euclidean norm satisfying Ap=b. The algorithm typically requires O(mn log(sqrt(n)/epsilon) + m**3) floating-point operations, generally less than the O(m**2 n) required by the classical schemes based on QR-decompositions or bidiagonalization. We present several numerical examples illustrating the performance of the algorithm.
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arxiv:0905.4745
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Geometric Langlands duality relates a representation of a simple Lie group $G^\vee$ to the cohomology of a certain moduli space associated with the dual group $G$. In this correspondence, a principal $SL_2$ subgroup of $G^\vee$ makes an unexpected appearance. Why this happens can be explained using gauge theory, as we will see in this article, with the help of the equations of Nahm and Bogomolny. (Based on a lecture at Geometry and Physics: Atiyah 80, Edinburgh, April 2009.)
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arxiv:0905.4795
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A number of DR-bar renormalization constants in softly broken SUSY-QCD are evaluated to three-loop level: the wave function renormalization constants for quarks, squarks, gluons, gluinos, ghosts, and epsilon-scalars, and the renormalization constants for the quark and gluino mass as well as for all cubic vertices. The latter allow us to derive the corresponding beta functions through three loops, all of which we find to be identical to the expression for the gauge beta function obtained by Jack, Jones, and North [Jack:1996vg] (see also Ref. [Pickering:2001aq]). This explicitely demonstrates the consistency of DRED with SUSY and gauge invariance, an important pre-requisite for precision calculations in supersymmetric theories.
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arxiv:0905.4807
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We obtain the Pairwise Summation Approximation (PSA) of the Casimir energy from first principles in the soft dielectric and soft diamagnetic limit, so we find that the PSA is an asymptotic approximation of the Casimir energy valid for large distances between the objects. We also obtain the PSA for the electromagnetic coupling part of the Casimir energy, so we are able to complete the PSA limit at a first time for the complete electromagnetic field.
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arxiv:0905.4825
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The corepresentation theory of continuous groups is presented without the assumption that the subgroup $G$ of the group with antilinear operations is unitary. The formulas of the corepresentation theory with unitary groups $G$ can be obtained from this presentation.
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arxiv:0905.4828
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Using data from FOCUS (E831) experiment at Fermilab, we present a model independent partial-wave analysis of the $K^-\pi^+$ S-wave amplitude from the decay $D^+ \to K^-\pi^+\pi^+$. The S-wave is a generic complex function to be determined directly from the data fit. The P- and D-waves are parameterized by a sum of Breit-Wigner amplitudes. The measurement of the S-wave amplitude covers the whole elastic range of the $K^-\pi^+$ system.
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arxiv:0905.4846
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We study the decay of a prepared state into non-flat continuum. We find that the survival probability $P(t)$ might exhibit either stretched-exponential or power-law decay, depending on non-universal features of the model. Still there is a universal characteristic time $t_0$ that does not depend on the functional form. It is only for a flat continuum that we get a robust exponential decay that is insensitive to the nature of the intra-continuum couplings. The analysis highlights the co-existence of perturbative and non-perturbative features in the local density of states, and the non-linear dependence of $1/t_0$ on the strength of the coupling.
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arxiv:0905.4934
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We address the following important question: how to distinguish Kitaev models experimentally realized on small lattices from other non-topological interacting spin models. Based on symmetry arguments and exact diagonalization, we show that a particularly characteristic pattern of spin-spin correlations survives despite finite size, open boundary and thermal effects. The pattern is robust against small residual perturbing interactions and can be utilized to distinguish the Kitaev interactions from other interactions such as antiferromagnetic Heisenberg interactions. The effect of external magnetic field is also considered and found to be not critical.
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arxiv:0906.0017
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We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the Weyl modules and of the irreducible finite--dimensional representations of such algebras, describe a block decomposition of the (non--semisimple) category of their finite--dimensional representations, and conclude with recent developments in the representation theory of multiloop algebras.
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arxiv:0906.0099
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Phase-space Lagrangian dynamics in ideal fluids (i.e, continua) is usually related to the so-called {\it ideal tracer particles}. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution. \ The goal of this paper is to show that the tracer-particle dynamics can be {\it exactly} established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) (Tessarotto \textit{et al.}, 2000-2008). As an example, the case of an incompressible Newtonian thermofluid is here considered.
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arxiv:0906.0146
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Applying random matrix theory to quantum transport in chaotic cavities, we develop a novel approach to computation of the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open channels. The method is based on the Selberg integral theory combined with the theory of symmetric functions and is applicable equally well for systems with and without time-reversal symmetry. We also compute higher-order cumulants and perform their detailed analysis. In particular, we establish an explicit form of the leading asymptotic of the cumulants in the limit of the large channel numbers. We derive further a general Pfaffian representation for the corresponding distribution functions. The Edgeworth expansion based on the first four cumulants is found to reproduce fairly accurately the distribution functions in the bulk even for a small number of channels. As the latter increases, the distributions become Gaussian-like in the bulk but are always characterized by a power-law dependence near their edges of support. Such asymptotics are determined exactly up to linear order in distances from the edges, including the corresponding constants.
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arxiv:0906.0161
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The purpose of this note is to prove a lower bound for the estimation of the memory parameter of a stationary long memory process. The memory parameter is defined here as the index of regular variation of the spectral density at 0. The rates of convergence obtained in the literature assume second order regular variation of the spectral density at zero. In this note, we do not make this assumption, and show that the rates of convergence in this case can be extremely slow. We prove that the log-periodogram regression (GPH) estimator achieves the optimal rate of convergence for Gaussian long memory processes.
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arxiv:0906.0180
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One of the primary goals of the RHIC Spin program is to determine the gluon polarization distribution within the proton. At leading order, $pp$ collisions involve a mixture of quark-quark, quark-gluon, and gluon-gluon scattering. In RHIC, the gluon-gluon and quark-gluon contributions dominate, making the accelerator an ideal tool to explore gluon polarization. The STAR experiment has measured the longitudinal double-spin asymmetry $A_{LL}$ for inclusive production of jets and pions, and for charged pion production opposite a jet, at $\sqrt{s} = 200 GeV$. The results provide valuable new constraints on the gluon polarization in the proton when included in a next-to-leading-order global analysis. The current status of the STAR measurements and the plans for future measurements will be discussed.
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arxiv:0906.0271
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Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available when the problem was discovered.
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arxiv:0906.0290
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Time series are presented for the class II methanol maser source G12.89+0.49, which has been monitored for nine years at the Hartebeesthoek Radio Astronomy Observatory. The 12.2 and 6.7 GHz methanol masers were seen to exhibit rapid, correlated variations on timescales of less than a month. Daily monitoring has revealed that the variations have a periodic component with a period of 29.5 days. The period seems to be stable over the 110 cycles spanned by the time series. There are variations from cycle to cycle, with the peak of the flare occurring anywhere within an eleven day window but the minima occur at the same phase of the cycle. Time delays of up to 5.7 days are seen between spectral features at 6.7 GHz and a delay of 1.1 day is seen between the dominant 12.2 GHz spectral feature and its 6.7 GHz counterpart.
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arxiv:0906.0295
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The symmetric interaction combinators are an equally expressive variant of Lafont's interaction combinators. They are a graph-rewriting model of deterministic computation. We define two notions of observational equivalence for them, analogous to normal form and head normal form equivalence in the lambda-calculus. Then, we prove a full abstraction result for each of the two equivalences. This is obtained by interpreting nets as certain subsets of the Cantor space, called edifices, which play the same role as Boehm trees in the theory of the lambda-calculus.
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arxiv:0906.0380
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This article introduces the problem of finding intrinsic torsion varieties associated to G-structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures are analysed on the Iwasawa manifold.
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arxiv:0906.0457
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We analyze structure of the world foreign currency exchange (FX) market viewed as a network of interacting currencies. We analyze daily time series of FX data for a set of 63 currencies, including gold, silver and platinum. We group together all the exchange rates with a common base currency and study each group separately. By applying the methods of filtered correlation matrix we identify clusters of closely related currencies. The clusters are formed typically according to the economical and geographical factors. We also study topology of weighted minimal spanning trees for different network representations (i.e., for different base currencies) and find that in a majority of representations the network has a hierarchical scale-free structure. In addition, we analyze the temporal evolution of the network and detect that its structure is not stable over time. A medium-term trend can be identified which affects the USD node by decreasing its centrality. Our analysis shows also an increasing role of euro in the world's currency market.
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arxiv:0906.0480
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Monolayers of colloidally synthesized cobalt-platinum nanoparticles of different diameters characterized by TEM (transmission electron microscopy) were deposited on structured silicon oxide substrates and characterized by SEM (scanning electron microscopy), GISAXS (grazing incidence x-ray scattering), and electric transport measurements. The highly ordered nanoparticle films show a thermally activated electron hopping between spatially adjacent particles at room temperature and Coulomb blockade at low temperatures. We present a novel approach to experimentally determine the particles charging energies giving values of 6.7-25.4 meV dependent on the particles size and independent of the interparticle distance. These observations are supported by FEM (finite element method) calculations showing the self-capacitance to be the determining value which only depends on the permittivity constant of the surrounding space and the particles radius.
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arxiv:0906.0500
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We study the non-linear evolution of baryon acoustic oscillations in the matter power spectrum and correlation function from the improved perturbation theory (PT). Based on the framework of renormalized PT, we apply the {\it closure approximation} that truncates the infinite series of loop contributions at one-loop order, and obtain a closed set of integral equations for power spectrum and non-linear propagator. The resultant integral expressions keep important non-perturbative properties which can dramatically improve the prediction of non-linear power spectrum. Employing the Born approximation, we then derive the analytic expressions for non-linear power spectrum and the predictions are made for non-linear evolution of baryon acoustic oscillations in power spectrum and correlation function. A detailed comparison between improved PT results and N-body simulations shows that a percent-level agreement is achieved in a certain range in power spectrum and in a rather wider range in correlation function. Combining a model of non-linear redshift-space distortion, we also evaluate the power spectrum and correlation function in correlation function. In contrast to the results in real space, the agreement between N-body simulations and improved PT predictions tends to be worse, and a more elaborate modeling for redshift-space distortion needs to be developed. Nevertheless, with currently existing model, we find that the prediction of correlation function has a sufficient accuracy compared with the cosmic-variance errors for future galaxy surveys with volume of a few (Gpc/h)^3 at z>=0.5.
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arxiv:0906.0507
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We start from Feynman`s idea to use negative probabilities to describe the two slit experiment and other quantum interfernce experiments. Formally by using negative probability distributions we can explain the results of the two slit experiment on the basis of the pure corpuscular picture of quantum mechnanics. However, negative probabilities are absurd objects in the framework of the standard Kolmogorov theory of probability. We present a large class of non-Kolmogorovean probability models where negative probabilities are well defined on the frequency basis. These are models with probabilities which belong to the so-called field of $p$-adic numbers. However, these models are characterized by correlations between trails. Therefore, we predict correlations between particles in interference experiments. In fact, our predictions are similar to the predictions of the so-called nonergodic interpretation of quantum mechanics, which was proposed by V. Buonomano. We propose the concrete experiments (in particular, in the framework of the neutron interferometry) to verify our predictions on the correlations.
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arxiv:0906.0509
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The ability to accumulate and retrieve entanglement in the fields of two remote cavities with pairs of two-level atoms is discussed. It is shown that this transfer and retrieval can be indeed ideal with a resonant interaction. The case of initial non-maximally entangled atomic pairs is also considered. This leads to the possibility of concentrating entanglement into a single pair at the retrieval stage. A teleportation protocol based on the same setup is presented. This makes possible teleportation with built-in entanglement concentration.
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arxiv:0906.0529
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Closed expressions are derived for resonant multidimensional X-ray spectroscopy using the quasiparticle nonlinear exciton representation of optical response. This formalism is applied to predict coherent four wave mixing signals which probe single and two core-hole states. Nonlinear X-ray signals are compactly expressed in terms of one- and two- particle Green's functions which can be obtained from the solution of Hedin-like equations at the $GW$ level.
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arxiv:0906.0551
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Upcoming facilities such as the Herschel Space Observatory or ALMA will deliver a wealth of molecular line observations of young stellar objects (YSOs). Based on line fluxes, chemical abundances can then be estimated by radiative transfer calculations. To derive physical properties from abundances, the chemical network needs to be modeled and fitted to the observations. This modeling process is however computationally exceedingly demanding, particularly if in addition to density and temperature, far UV (FUV) irradiation, X-rays, and multi-dimensional geometry have to be considered. We develop a fast tool, suitable for various applications of chemical modeling in YSOs. A grid of the chemical composition of the gas having a density, temperature, FUV irradiation and X-ray flux is pre-calculated as a function of time. A specific interpolation approach is developed to reduce the database to a feasible size. Published models of AFGL 2591 are used to verify the accuracy of the method. A second benchmark test is carried out for FUV sensitive molecules. The novel method for chemical modeling is more than 250,000 times faster than direct modeling and agrees within a mean factor of 1.35. The tool is distributed for public use. In the course of devloping the method, the chemical evolution is explored: We find that X-ray chemistry in envelopes of YSOs can be reproduced by means of an enhanced cosmic-ray ionization rate. We further find that the abundance of CH+ in low-density gas with high ionization can be enhanced by the recombination of doubly ionized carbon (C++) and suggest a new value for the initial abundance of the main sulphur carrier in the hot-core.
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arxiv:0906.0584
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We show that any direction in the plane occurs as the unique non-expansive direction of a \mathbb{Z}^{2} action, answering a question of Boyle and Lind. In the case of rational directions, the subaction obtained is non-trivial. We also establish that a cellular automaton can have zero Lyapunov exponents and at the same time act sensitively; and more generally, for any positive real \theta there is a cellular automaton acting on an appropriate subshift with \lambda^{+}=-\lambda^{-}=\theta.
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arxiv:0906.0609
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We studied the microwave assisted magnetic reversal of 65 nm by 71 nm elliptical Ni80Fe20 nanomagnets. Hysteresis curves were measured by magneto-optical Kerr effect for a range of microwave frequencies and amplitudes. The coercive field Hc was reduced by 26% for an rf field of 0.08Hc when the microwave frequency coincided with the minimum of the experimentally determined ferromagnetic resonance frequency with varying dc field. The experimental results for the fractional reduction in Hc with rf field amplitude are in good agreement with numerical simulations for an array of interacting macrospins with a physically realistic shape anisotropy distribution
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arxiv:0906.0626
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There is two group actions on the Fano scheme of lines such that the quotient becomes an irreducible symplectic manifold. We showed that both quotients are birational to the generalized Kummer variety or the 2-points Hilbert scheme of a K3 surface.
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arxiv:0906.0654
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We analyze momentarily static initial data sets of the gravitational field produced by two-point sources in five-dimensional Kaluza-Klein spacetimes. These initial data sets are characterized by the mass, the separation of sources and the size of a extra dimension. Using these initial data sets, we discuss the condition for black hole formation, and propose a new conjecture which is a hybrid of the four-dimensional hoop conjecture and the five-dimensional hyperhoop conjecture. By using the new conjecture, we estimate the cross section of black hole formation due to collisions of particles in Kaluza-Klein spacetimes. We show that the mass dependence of the cross section gives us information about the size and the number of the compactified extra dimensions.
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arxiv:0906.0689
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The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next--nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin--spin correlations. Findings on the variation of the critical cumulant with the ratio of the two interaction strengths are compared to related recent results based on renormalization group calculations.
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arxiv:0906.0721
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Propagating, directionally dependent, polarized spin-currents are created in an anisotropic planar semiconductor microcavity, via Rayleigh scattering of optically injected polaritons in the optical spin Hall regime. The influence of anisotropy results in the suppression or enhancement of the pseudospin precession of polaritons scattered into different directions. This is exploited to create intense spin currents by excitation on top of localized defects. A theoretical model considering the influence of the total effective magnetic field on the polariton pseudospin quantitatively reproduces the experimental observations.
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arxiv:0906.0746
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The existence of two stationary solutions of the nonlinear Boltzmann equation for inelastic hard spheres or disks is investigated. They are restricted neither to weak dissipation nor to small gradients. The one-particle distribution functions are assumed to have an scaling property, namely that all the position dependence occurs through the density and the temperature. At the macroscopic level, the state corresponding to both is characterized by uniform pressure, no mass flow, and a linear temperature profile. Moreover, the state exhibits two peculiar features. First, there is a relationship between the inelasticity of collisions, the pressure, and the temperature gradient. Second, the heat flux can be expressed as being linear in the temperature gradient, i.e. a Fourier-like law is obeyed. One of the solutions is singular in the elastic limit. The theoretical predictions following from the other one are compared with molecular dynamics simulation results and a good agreement is obtained in the parameter region in which the Fourier state can be actually observed in the simulations, namely not too strong inelasticity.
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arxiv:0906.0747
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The Lefschetz fixed point theorem and its converse have many generalizations. One of these generalizations is to endomorphisms of a space relative to a fixed subspace. In this paper we define relative Lefschetz numbers and Reidemeister traces using traces in bicategories with shadows. We use the functoriality of this trace to identify different forms of these invariants and to prove a relative Lefschetz fixed point theorem and its converse.
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arxiv:0906.0762
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A graphene $pn$ junction is studied theoretically in the presence of both intrinsic and Rashba spin-orbit couplings. We show that a crossover from perfect reflection to perfect transmission is achieved at normal incidence by tuning the perpendicular electric field. By further studying angular dependent transmission, we demonstrate that perfect reflection at normal incidence can be clearly distinguished from trivial band gap effects. We also investigate how spin-orbit effects modify the conductance and the Fano factor associated with a potential step in both $nn$ and $np$ cases.
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arxiv:0906.0775
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We give a precise and concise formulation of the orientifold construction in Type II superstring theory. Our results include anomaly cancellation on the worldsheet and a spacetime computation of the background Ramond-Ramond charge.
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arxiv:0906.0795
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The minimum free-energy path (MFEP) is the most probable route of the nucleation process on the multidimensional free-energy surface. In this study, the phase-field equation is used as a mathematical tool to deduce the minimum free-energy path (MFEP) of homogeneous nucleation. We use a simple square-gradient free-energy functional with a quartic local free-energy function as an example and study the time evolution of a single nucleus placed within a metastable environment. The time integration of the phase-field equation is performed using the numerically efficient cell-dynamics method. By monitoring the evolution of the size of the nucleus and the free energy of the system simultaneously, we can easily deduce the free-energy barrier as a function of the size of the sub- and the super-critical nucleus along the MFEP.
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arxiv:0906.0805
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We examine charge fractionalization by chiral separation in a one-dimensional fermion system described by Luttinger liquid theory. The focus is on the question of whether the fractional charges are quantum mechanically sharp, and in the analysis we make a distinction between the global charge, which is restricted by boundary conditions, and the local charge where a background contribution is subtracted. We show, by way of examples, that fractional charges of arbitrary values, all which are quantum mechanically sharp, can be introduced by different initial conditions. Since the system is gapless, excitations of arbitrary low frequency contribute to the fluctuations, it is important to make a precise definition of sharp charges, and this we we do by subtraction of the ground state contribution. We very briefly comment on the relevance of our analysis for proposed experiments.
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arxiv:0906.0811
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The basis of the so-called Zenon effect in Quantum Mechanics, is the limiting behavior of the unitary solution of Schroedinger's equation, under repeated measurments. We examine the limit of a sequence of operators complosed by a usual operator and a projection operator.
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arxiv:0906.0830
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The supergiant fast X-ray transient source IGR J16479-4514 was observed in outburst two times with Swift. Its quiescent state was investigated in-depth only once in 2008 through a relatively long pointed observation with XMM-Newton. The latter observation was taken about 1.7 days after the outburst in 2008, and showed an X-ray eclipse-like event, likely caused by the supergiant companion. At present, this is the only supergiant fast X-ray transient that displayed an evidence for an X-ray eclipse. Here we carry out a comparison between the most recent outburst of IGRJ16479-4514, caught by Swift on 29 January 2009 and those detected previously from this source. The decay from the outbursts in 2005, 2008 and 2009 presents many similarities, and suggests a common mechanism that modulates the mass accretion rate onto the neutron star in IGRJ16479-4514.
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arxiv:0906.0883
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We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry or four-fold symmetry. In this work - the first of a pair of articles - we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot's internal dynamics. The second article addresses symmetry-breaking by displacement of the leads. Using semiclassics, we identify the origin of the symmetry-induced interference effects that contribute to weak-localization corrections and universal conductance fluctuations. For perfect spatial symmetry, we recover results previously found using the random-matrix theory conjecture. We then go on to show how the results are affected by asymmetries in the dot, magnetic fields and decoherence. In particular, the symmetry-asymmetry crossover is found to be described by a universal dependence on an asymmetry parameter $\gamma_{asym}$. However, the form of this parameter is very different depending on how the dot is deformed away from spatial symmetry. Symmetry-induced interference effects are completely destroyed when the dot's boundary is globally deformed by less than an electron wavelength. In contrast, these effects are only reduced by a finite amount when a part of the dot's boundary smaller than a lead-width is deformed an arbitrarily large distance.
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arxiv:0906.0891
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For each closed, positive (1,1)-current \omega on a complex manifold X and each \omega-upper semicontinuous function \phi on X we associate a disc functional and prove that its envelope is equal to the supremum of all \omega-plurisubharmonic functions dominated by \phi. This is done by reducing to the case where \omega has a global potential. Then the result follows from Poletsky's theorem, which is the special case \omega=0. Applications of this result include a formula for the relative extremal function of an open set in X and, in some cases, a description of the \omega-polynomial hull of a set.
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arxiv:0906.0902
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In this paper, we analyze the temporal evolution of the age-dependent force of infection and incidence of rubella, after the introduction of a very specific vaccination programme in a previously nonvaccinated population where rubella was in endemic steady state. We deduce an integral equation for the age-dependent force of infection, which depends on a number of parameters that can be estimated from the force of infection in steady state prior to the vaccination program. We present the results of our simulations, which are compared with observed data. We also examine the influence of contact patterns among members of a community on the age-dependent intensity of transmission of rubella and on the results of vaccination strategies. As an example of the theory proposed, we calculate the effects of vaccination strategies for four communities from Caieiras (Brazil), Huixquilucan (Mexico), Finland and the United Kingdom. The results for each community differ considerably according to the distinct intensity and pattern of transmission in the absence of vaccination. We conclude that this simple vaccination program is not very efficient (very slow) in the goal of eradicating the disease. This gives support to a mixed strategy, proposed by Massad et al., accepted and implemented by the government of the State of Sao Paulo, Brazil.
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arxiv:0906.0917
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The Fermi g_F(x,p) function provides a phase space description of quantum mechanics conceptually different from that based on the the Wigner function W(x,p). In this paper, we show that for a peaked wave packet the g_F(x,p)=0 curve approximately corresponds to a phase space contour level of the Wigner function and provides a satisfactory description of the wave packet's size and shape. Our results show that the Fermi function is an interesting tool to investigate quantum fluctuations in the semiclassical regime.
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arxiv:0906.0925
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It is generally believed that coupling the graviton (a classical Fierz-Pauli massless spin-2 field) to its own energy-momentum tensor successfully recreates the dynamics of the Einstein field equations order by order; however the validity of this idea has recently been brought into doubt [1]. Motivated by this, we present a graviton action for which energy-momentum self-coupling is indeed consistent with the Einstein field equations. The Hilbert energy-momentum tensor for this graviton is calculated explicitly and shown to supply the correct second-order term in the field equations; in contrast, the Fierz-Pauli action fails to supply the correct term. A formalism for perturbative expansions of metric-based gravitational theories is then developed, and these techniques employed to demonstrate that our graviton action is a starting point for a straightforward energy-momentum self-coupling procedure that, order by order, generates the Einstein-Hilbert action (up to a classically irrelevant surface term). The perturbative formalism is extended to include matter and a cosmological constant, and interactions between perturbations of a free matter field and the gravitational field are studied in a vacuum background. Finally, the effect of a non-vacuum background is examined, and the graviton is found to develop a non-vanishing ``mass-term'' in the action.
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arxiv:0906.0926
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The well-established correlations between the mass of massive black holes (BHs) in the nuclei of most studied galaxies and various global properties of their hosting galaxy lend support to the idea that dwarf galaxies and globular clusters could also host a BH in their centers. Direct kinematic detection of BHs in dwarf spheroidal (dSph) galaxies are seriously hindered by the small number of stars inside the gravitational influence region of the BH. The aim of this Letter is to establish an upper dynamical limit on the mass of the putative BH in the Ursa Minor (UMi) dSph galaxy. We present direct N-body simulations of the tidal disruption of the dynamical fossil observed in UMi, with and without a massive BH. We find that the observed substructure is incompatible with the presence of a massive BH of (2-3)x10^4 Msun within the core of UMi. These limits are consistent with the extrapolation of the M_{BH}-sigma relation to the M_{BH}<10^6 Msun regime. We also show that the BH may be off-center with respect to the center of symmetry of the whole galaxy.
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arxiv:0906.0951
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For any non-degenerate, quasi-homogeneous hypersurface singularity W and an admissible group of diagonal symmetries G, Fan, Jarvis, and Ruan have constructed a cohomological field theory which is a candidate for the mathematical structure behind the Landau-Ginzburg A-model. When using the orbifold Milnor ring of a singularity W as a B-model, and the Frobenius algebra H_{W,G} constructed by Fan, Jarvis, and Ruan, as an A-model, the following conjecture is obtained: For a quasi-homogeneous singularity W and a group G of symmetries of W, there is a dual singularity W^T such that the orbifold A-model of W/G is isomorphic to the B-model of W^T. I will show that this conjecture holds for a two-dimensional invertible loop potential $W$ with its maximal group of diagonal symmetries $G_{W}$.
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arxiv:0906.0970
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We study a polymer model on hierarchical lattices very close to the one introduced and studied in \cite{DGr, CD}. For this model, we prove the existence of free energy and derive the necessary and sufficient condition for which very strong disorder holds for all $\gb$, and give some accurate results on the behavior of the free energy at high-temperature. We obtain these results by using a combination of fractional moment method and change of measure over the environment to obtain an upper bound, and second moment method to get a lower bound. We also get lower bounds on the fluctuation exponent of $\log Z_n$, and study the infinite polymer measure in the weak disorder phase.
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arxiv:0906.0992
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We report on the finding of a correlation between galaxies' past star formation activity and the degree to which neighbouring galaxies rotation axes are aligned. This is obtained by cross-correlating star formation histories, derived with MOPED, and spin direction (chirality), as determined by the Galaxy Zoo project, for a sample of SDSS galaxies. Our findings suggest that spiral galaxies which formed the majority of their stars early (z > 2) tend to display coherent rotation over scales of ~10 Mpc/h. The correlation is weaker for galaxies with significant recent star formation. We find evidence for this alignment at more than the 5-sigma level, but no correlation with other galaxy stellar properties. This finding can be explained within the context of hierarchical tidal-torque theory if the SDSS galaxies harboring the majority of the old stellar population where formed in the past, in the same filament and at about the same time. Galaxies with significant recent star formation instead are in the field, thus influenced by the general tidal field that will align them in random directions or had a recent merger which would promote star formation, but deviate the spin direction.
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arxiv:0906.0994
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It is well established that in a market with inclusion of a risk-free asset the single-period mean-variance efficient frontier is a straight line tangent to the risky region, a fact that is the very foundation of the classical CAPM. In this paper, it is shown that in a continuous-time market where the risky prices are described by Ito's processes and the investment opportunity set is deterministic (albeit time-varying), any efficient portfolio must involve allocation to the risk-free asset at any time. As a result, the dynamic mean-variance efficient frontier, though still a straight line, is strictly above the entire risky region. This in turn suggests a positive premium, in terms of the Sharpe ratio of the efficient frontier, arising from the dynamic trading. Another implication is that the inclusion of a risk-free asset boosts the Sharpe ratio of the efficient frontier, which again contrasts sharply with the single-period case.
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arxiv:0906.0999
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We study charge and energy transport in a quasi-1D magnetic wire in the presence of magnetic textures. The energy flows can be expressed in a fashion similar to charge currents, leading to new energy-current induced spin torques. In analogy to charge currents, we can identify two reciprocal effects: spin-transfer torque on the magnetic order parameter induced by energy current and the Berry-phase gauge field induced energy flow. In addition, we phenomenologically introduce new $\beta-$like viscous coupling between magnetic dynamics and energy current into the LLG equation, which originates from spin mistracking of the magnetic order. We conclude that the new viscous term should be important for the thermally induced domain wall motion. We study the interplay between charge and energy currents and find that many of the effects of texture motion on the charge currents can be replicated with respect to energy currents. For example, the moving texture can lead to energy flows which is an analogue of the electromotive force in case of charge currents. We suggest a realization of cooling effect by magnetic texture dynamics.
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arxiv:0906.1002
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Normalized Laplacian matrices of graphs have recently been studied in the context of quantum mechanics as density matrices of quantum systems. Of particular interest is the relationship between quantum physical properties of the density matrix and the graph theoretical properties of the underlying graph. One important aspect of density matrices is their entanglement properties, which are responsible for many nonintuitive physical phenomena. The entanglement property of normalized Laplacian matrices is in general not invariant under graph isomorphism. In recent papers, graphs were identified whose entanglement and separability properties are invariant under isomorphism. The purpose of this note is to characterize the set of graphs whose separability is invariant under graph isomorphism. In particular, we show that this set consists of $K_{2,2}$, $\overline{K_{2,2}}$ and all complete graphs.
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arxiv:0906.1016
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The current controversies about the existence of an intermediate 'beta' phase of BiFeO_3 and the high temperature paraelectric 'gamma' phase are resolved by studying the sequence of ferroic transitions in 0.8BiFeO_3-0.2Pb(Fe_1/2Nb_1/2)O_3 (BF-0.2PFN) with lowered transition temperature. It is shown that the room temperature ferroelectric phase of 0.8BF-0.2PFN in the R3c space group transforms to the paraelectric/paraelastic cubic (Pm-3m) phase directly without any intermediate 'beta' phase reported in the literature. This transition is of first order type as confirmed by the coexistence of R3c and Pm-3m phases over a 100K range and a discontinuous change in the unit cell volume.
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arxiv:0906.1106
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We propose a scheme to dynamically create a supersolid state in an optical lattice, using an attractive mixture of mass-imbalanced bosons. Starting from a "molecular" quantum crystal, supersolidity is induced dynamically as an out-of-equilibrium state. When neighboring molecular wavefunctions overlap, both bosonic species simultaneously exhibit quasi-condensation and long-range solid order, which is stabilized by their mass imbalance. Supersolidity appears in a perfect one-dimensional crystal, without the requirement of doping. Our model can be realized in present experiments with bosonic mixtures that feature simple on-site interactions, clearing the path to the observation of supersolidity.
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arxiv:0906.1110
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The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz. We present another proof of the result of N.J.S. Hughes \cite{1} on Steinitz' exchange theorem for infinite bases. In our proof we assume Kuratowski-Zorn Maximum Principle instead of well ordering. We present some examples of dependence spaces of general nature with theirs possible applications of the result in other as linear or universal algebra domains of mathematical sciences. The lecture was presented on 77th Workshop on General Algebra, 24th Conference for Young Algebraists in Potsdam (Germany) on 21st March 2009.
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arxiv:0906.1132
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An LR-structure on a Lie algebra is a bilinear product, satisfying certain commutativity relations, and which is compatible with the Lie product. LR-structures arise in the study of simply transitive affine actions on Lie groups. In particular one is interested in the question which Lie algebras admit a complete LR-structure. In this paper we show that a Lie algebra admits a complete LR-structure if and only if it admits any LR-structure.
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arxiv:0906.1151
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It is well known that the dynamics of a quantum system is always non-adiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching. However, we propose here a possible situation where the dynamics of a quantum system in passage across quantum critical regions is adiabatic and the defect density decays exponentially. This is achieved by incorporating additional interactions which lead to quantum critical behavior and gapless phases but do not participate in the time evolution of the system. To illustrate the general argument, we study the defect generation in the quantum critical dynamics of a spin-1/2 anisotropic quantum XY spin chain with three spin interactions and a linearly driven staggered magnetic field.
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arxiv:0906.1161
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A graph $G(V,E)$ is a threshold graph if there exist non-negative reals $w_v, v \in V$ and $t$ such that for every $U \subseteq V$, $\sum_{v \in U} w_v\leq t$ if and only if $U$ is a stable set. The {\it threshold dimension} of a graph $G(V,E)$, denoted as $t(G)$, is the smallest integer $k$ such that $E$ can be covered by $k$ threshold spanning subgraphs of $G$. A permutation graph is a graph that can be represented as the intersection graph of a family of line segments that connect two parallel lines in the Euclidean plane. In this paper we will show that if $G$ is a permutation graph then $t(G) \leq \alpha(G)$ (where $\alpha(G)$ is the cardinality of maximum independent set in $G$) and this bound is tight. As a corollary we will show that $t(G) \leq \frac{n}{2}$ where $n$ is the number of vertices in the permutation graph $G$. This bound is also tight.
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arxiv:0906.1165
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We examine the majorization properties of general thermal-like mixed states depending on a set of parameters. Sufficient conditions which ensure the increase in mixedness, and hence of any associated entropic form, when these parameters are varied, are identified. We then discuss those exhibiting a power law distribution, showing that they can be characterized by two distinct mixing parameters, one associated with temperature and the other with the non-extensivity index q. Illustrative numerical results are also provided.
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arxiv:0906.1216
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We consider the decelerating shock instability of Vishniac for a finite layer of constant density. This serves both to clarify which aspects of the Vishniac instability mechanism depend on compressible effects away from the shock front and also to incorporate additional effects of finite layer thickness. This work has implications for experiments attempting to reproduce the essential physics of astrophysical shocks, in particular their minimum necessary lateral dimensions to contain all the relevant dynamics.
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arxiv:0906.1222
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In this paper, using the theory of category, we generalize known properties of symmetric polynomials and functions and characterize the multi-indicial symmetric functions. Examples have been given on Schur functions.
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arxiv:0906.1252
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We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also consider continuous modification of Gauss density in $\R^2$. Finally, we give a list of related open questions.
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arxiv:0906.1256
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We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry. Starting from a remark of Rieffel on compact manifolds, we first show that on any - i.e. non-necessary compact - complete Riemannian spin manifolds, the two distances coincide. Then, on convex manifolds in the sense of Nash embedding, we provide some natural upper and lower bounds to the distance between any two probability distributions. Specializing to the Euclidean space $R^n$, we explicitly compute the distance for a particular class of distributions generalizing Gaussian wave packet. Finally we explore the analogy between the spectral and the Wasserstein distances in the noncommutative case, focusing on the standard model and the Moyal plane. In particular we point out that in the two-sheet space of the standard model, an optimal-transport interpretation of the metric requires a cost function that does not vanish on the diagonal. The latest is similar to the cost function occurring in the relativistic heat equation.
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arxiv:0906.1267
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Stellar astrospheres--the plasma cocoons carved out of the interstellar medium by stellar winds--are continually influenced by their passage through the fluctuating interstellar medium (ISM). Inside dense interstellar regions, an astrosphere may be compressed to a size smaller than the liquid-water habitable zone distance. Habitable planets then enjoy no astrospheric buffering from the full flux of Galactic cosmic rays and interstellar dust and gas, a situation we call ``descreening.'' Recent papers (Yeghikyan and Fahr, Pavlov et al.) have suggested such global consequences as severe ozone depletion and glaciation. Using a ram-pressure balance model that includes gravitational focusing of the interstellar flow, we compute the size of the astrosphere in the apex direction as a function of parent star mass. We derive a dependence on the parent-star mass M due to gravitational focusing for densities larger than about 100 (M/M_\odot)^{-2} cm^{-3}. We calculate the interstellar densities required to descreen planets in the habitable zone of solar- and subsolar-mass stars and find a critical descreening density of roughly 600 (M/M_\odot)^{-2} cm^{-3} for the Sun's velocity relative to the local ISM. Finally, we estimate from ISM observations the frequency of descreening encounters as 1--10 Gyr^{-1} for solar-type stars and 10^2--10^9 times smaller for M stars. Given this disparity, we conclude that M star habitable-zone planets are virtually never exposed to the severe effects discussed by Yeghikyan and Fahr and Pavlov et al.
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arxiv:0906.1274
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We propose that stable two-dimensional (2D) ferromagnets can be made of regular single-layered lattices of single-molecule nanomagnets with enough uniaxial magnetic anisotropy on appropriate substrates by controlling the inter-nanomagnet magnetic interaction. Our Monte Carlo simulated results show that such ideal 2D ferromagnets are thermodynamically stable when the anisotropy is strong enough. If the anisotropy energy equals 80 K, approximately that of the Mn12, the T_c varies from zero to 15 K depending on different inter-nanomagnet coupling constants. Such stable spin systems, experimentally accessible, should be promising for information applications.
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arxiv:0906.1298
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The peak-background split argument is commonly used to relate the abundance of dark matter halos to their spatial clustering. Testing this argument requires an accurate determination of the halo mass function. We present a Maximum Likelihood method for fitting parametric functional forms to halo abundances which differs from previous work because it does not require binned counts. Our conclusions do not depend on whether we use our method or more conventional ones. In addition, halo abundances depend on how halos are defined. Our conclusions do not depend on the choice of link length associated with the friends-of-friends halo-finder, nor do they change if we identify halos using a spherical overdensity algorithm instead. The large scale halo bias measured from the matter-halo cross spectrum b_x and the halo autocorrelation function b_xi (on scales k~0.03h/Mpc and r ~50 Mpc/h) can differ by as much as 5% for halos that are significantly more massive than the characteristic mass M*. At these large masses, the peak background split estimate of the linear bias factor b1 is 3-5% smaller than b_xi, which is 5% smaller than b_x. We discuss the origin of these discrepancies: deterministic nonlinear local bias, with parameters determined by the peak-background split argument, is unable to account for the discrepancies we see. A simple linear but nonlocal bias model, motivated by peaks theory, may also be difficult to reconcile with our measurements. More work on such nonlocal bias models may be needed to understand the nature of halo bias at this level of precision.
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arxiv:0906.1314
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We propose a simplified model of outflow/jet driven by the Blandford-Payne (BP) process from advection dominated accretion flows (ADAF) and derive the expressions of the BP power and disk luminosity based on the conservation laws of mass, angular momentum and energy. We fit the 2--10 keV luminosity and kinetic power of 15 active galactic nucleus (AGNs) of sub-Eddington luminosity. It is found that there exists an anti-correlation between the accretion rate and the advection parameter, which could be used to explain the correlation between Eddington-scaled kinetic power and bolometric luminosity of the 15 samples. In addition, the Ledlow-Owen relation for FR I/II dichotomy is re-expressed in a parameter space consisting of logarithm of dimensionless accretion rate versus that of the BH mass. It turns out that the FR I/II dichotomy is determined mainly by the dimensionless accretion rate, being insensitive to the BH mass. And the dividing accretion rate is less than the critical accretion rate for ADAFs, suggesting that FR I sources are all in the ADAF state.
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arxiv:0906.1323
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We review various cosmological models with a local underdense region (local void) and the averaged models with the backreaction of inhomogeneities, which have been proposed to explain (without assuming a positive cosmological constant) the observed accelerating behaviors appearing in the magnitude-redshift relation of SNIa. To clarify their reality, we consider their consistency with the other observational studies such as CMB temperature anisotropy, baryon acoustic oscillation, kinematic Sunyaev-Zeldovich effect, and so on. It is found as a result that many inhomogeneous models seem to be ruled out and only models with the parametrs in the narrow range remain to be examined, and that, unless we assume very high amplitudes of perturbations or gravitational energies, the averaged models cannot have the accelerated expansion and the fitted effective Lambda has not the value necessary for the observed acceleration.
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arxiv:0906.1325
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A variety of analytical techniques suggest that quantum fluctuations lead to a fundamental instability of the Fermi liquid that drives ferromagnetic transitions first order at low temperatures. We present both analytical and numerical evidence that, driven by the same quantum fluctuations, this first order transition is pre-empted by the formation of an inhomogeneous magnetic phase. This occurs in a manner that is closely analogous to the formation of the inhomogeneous superconducting Fulde-Ferrel-Larkin-Ovchinnikov state. We derive these results from a field theoretical approach supplemented with numerical Quantum Monte Carlo simulations. Our analytical approach represents a considerable simplification over diagrammatic methods, makes contact with older analyses of the unitarity limit, and enables a simple physical picture to emerge.
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arxiv:0906.1347
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Results are presented of extended and refined optical identification of 181 radio/X-ray sources in the RASS-Green Bank (RGB) catalog which have been spectroscopically observed in the Sloan digital sky survey (SDSS) DR5. For 72 sources, the identifications for are presented for the first time. It is confirmed that the majority of strong radio/X-ray emitters are radio-loud active galactic nuclei (AGNs), particularly blazars. Taking advantage of the high spectral quality and resolution and our refined spectral modeling, we are able to disentangle narrow line radio galaxies (NLRGs), as vaguely termed in most previous identification work, into Seyfert II galaxies and LINERs, based on the standard emission line diagnostics. The NLRGs in the RGB sample, mostly belonging to `weak line radio galaxies', are found have optical spectra consistent predominantly with LINERs, and only a small fraction with Seyfert II galaxies. A small number of LINERs have radio power as high as $10^{23}-10^{26}$ \whz at 5 GHz, being among the strongest radio emitting LINERs known so far. Two sources are identified with radio-loud narrow line Seyfert 1 galaxies (NLS1s), a class of rare objects. The presence is also confirmed of flat-spectrum radio quasars with the radio--optical--X-ray effective spectral indices similar to those of High-energy peaked BL Lac (HBL), albeit it is yet a debate as to whether this is the case for their actual spectral energy distributions.
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arxiv:0906.1361
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Using ideas from shape theory we embed the coarse category of metric spaces into the category of direct sequences of simplicial complexes with bonding maps being simplicial. Two direct sequences of simplicial complexes are equivalent if one of them can be transformed to the other by contiguous factorizations of bonding maps and by taking infinite subsequences. That embedding can be realized by either Rips complexes or analogs of Roe's anti-\v\{C}ech approximations of spaces. In that model the asymptotic dimension being at most n means that for each k there is m > k such that the bonding map from K_k to K_m factors (up to contiguity) through an n-dimensional complex. One can give a similar characterization of Property A of G.Yu. Using our approach we give a simple proof of a characterization of geodesic spaces that are coarsely equivalent to simplicial trees (a result of Fujiwara and Whyte).
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arxiv:0906.1372
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We investigate the effect of the intrinsic spin of a fundamental spinor field on the surrounding spacetime geometry. We show that despite the lack of a rotating stress-energy source (and despite claims to the contrary) the intrinsic spin of a spin-half fermion gives rise to a frame-dragging effect analogous to that of orbital angular momentum, even in Einstein-Hilbert gravity where torsion is constrained to be zero. This resolves a paradox regarding the counter-force needed to restore Newton's third law in the well known spin-orbit interaction. In addition, the frame-dragging effect gives rise to a {\it long-range} gravitationally mediated spin-spin dipole interaction coupling the {\it internal} spins of two sources. We argue that despite the weakness of the interaction, the spin-spin interaction will dominate over the ordinary inverse square Newtonian interaction in any process of sufficiently high-energy for quantum field theoretical effects to be non-negligible.
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arxiv:0906.1385
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In this paper, we present a theoretical justification of the 0-1 test for chaos. In particular, we show that with probability one, the test yields 0 for periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics.
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arxiv:0906.1415
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In this paper we address practical aspects of the implementation of the 0-1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which significantly increases its sensitivity. The test can be viewed as a method to distill a binary quantity from the power spectrum. The implementation is guided by recent results from the theoretical justification of the test as well as by exploring better statistical methods to determine the binary quantities. We give several examples to illustrate the improvement.
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arxiv:0906.1418
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A simulation study of the magnetic electron drift vortex (MEDV) mode turbulence in a magnetoplasma in the presence of inhomogeneities in the plasma temperature and density, as well as in the external magnetic field, is presented. The study shows that the influence of the magnetic field inhomogeneity is to suppress streamer-like structures observed in previous simulation studies without background magnetic fields. The MEDV mode turbulence exhibits non-universal (non-Kolmogorov type) spectra for different sets of the plasma parameters. In the presence of an inhomogeneous magnetic field, the spectrum changes to a 7/3 power law, which is flatter than without magnetic field gradients. The relevance of this work to laser-produced plasmas in the laboratory is briefly mentioned.
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arxiv:0906.1423
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The tangential map is a map on the set of smooth planar curves. It satisfies the 3D-consistency property and is closely related to some well-known integrable equations.
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arxiv:0906.1425
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We establish an explicit algebra isomorphism between the quantum reflection algebra for the $U_q(\hat{sl_2})$ R-matrix and a new type of current algebra. These two algebras are shown to be two realizations of a special case of tridiagonal algebras (q-Onsager).
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arxiv:0906.1482
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