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The experimentally observed, ambipolar field-effect characteristics of Mott insulators are reproduced in the one-dimensional Hubbard model attached to a tight-binding model for source and drain electrodes. The formation of Schottky barriers, originating from the work-function difference, is taken into account by a potential satisfying the Poisson equation with an appropriate boundary condition. Then, these field-effect characteristics are shown to be related by unique current-voltage characteristics of metal-Mott-insulator interfaces.
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arxiv:0710.3533
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We study quark thermal recombination as a function of energy density during the evolution of a heavy-ion collision in a numerical model that reproduces aspects of QCD phenomenology. We show that starting with a set of free quarks (or quarks and antiquarks) the probability to form colorless clusters of three quarks differs from that to form colorless clusters of quark-antiquark and that the former has a sharp jump at a critical energy density whereas the latter transits smoothly from the low to the high energy density domains. We interpret this as a quantitative difference in the production of baryons and mesons with energy density. We use this approach to compute the proton and pion spectra in a Bjorken scenario that incorporates the evolution of these probabilities with energy density, and therefore with proper time. From the spectra, we compute the proton to pion ratio and compare to data at the highest RHIC energies. We show that for a standard choice of parameters, this ratio reaches one, though the maximum is very sensitive to the initial evolution proper time.
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arxiv:0710.3629
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We study the cyclic $U(\mathfrak{gl}_n)$-module generated by the $l$-th power of the $\alpha$-determinant. When $l$ is a non-negative integer, for all but finite exceptional values of $alpha$, one shows that this cyclic module is isomorphic to the $n$-th tensor space $(S^l(\mathbb{C}^n))^{\otimes n}$ of the symmetric $l$-th tensor space of $\mathbb{C}^n$. If $alpha$ is exceptional, then the structure of the module changes drastically, i.e. some irreducible representations which are the irreducible components of the decomposition of $(S^l(\mathbb{C}^n))^{\otimes n}$ disappear in the decomposition of the cyclic module. The degeneration of each isotypic component of the cyclic module is described by a matrix whose size is given by a Kostka number and entries are polynomials in $alpha$ with rational coefficients. As a special case, we determine the matrix in a full of the detail for the case where $n=2$; the matrix becomes a scalar and is essentially given by the classical Jacobi polynomial. Moreover, we prove that these polynomials are unitary.
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arxiv:0710.3669
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In this paper, mainly using the convexity of the function $\frac{a^x-b^x}{c^x-d^x}$ and convexity or concavity of the function $\ln\frac{a^x-b^x}{c^x-d^x}$ on the real line, where $a>b\geq c>d>0$ are fixed real numbers, we obtain some important relations between various important means of these numbers. Also, we apply the obtained results to Ky Fan type inequalities and get some new refinements.
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arxiv:0710.3681
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We study the joint spectral properties of photon pairs generated by spontaneous parametric down-conversion in a one-dimensional nonlinear photonic crystal in a collinear, degenerate, type-II geometry. We show that the photonic crystal properties may be exploited to compensate for material dispersion and obtain photon pairs that are nearly factorable, in principle, for arbitrary materials and spectral regions, limited by the ability to fabricate the nonlinear crystal with the required periodic variation in the refractive indices for the ordinary and extraordinary waves.
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arxiv:0710.3745
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We present results of the search for coincident burst excitations over a 24 hours long data set collected by AURIGA, EXPLORER, NAUTILUS and Virgo detectors during September 2005. The search of candidate triggers was performed independently on each of the data sets from single detectors. We looked for two-fold time coincidences between these candidates using an algorithm optimized for a given population of sources and we calculated the efficiency of detection through injections of templated signal waveforms into the streams of data. To this purpose we have considered the case of signals shaped as damped sinusoids coming from the galactic center direction. In this framework our method targets an optimal balance between high efficiency and low false alarm rate, aiming at setting confidence intervals as stringent as possible in terms of the rate of the selected source models.
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arxiv:0710.3752
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Procyon A is a bright F5IV star in a binary system. Although the distance, mass and angular diameter of this star are all known with high precision, the exact evolutionary state is still unclear. Evolutionary tracks with different ages and different mass fractions of hydrogen in the core pass, within the errors, through the observed position of Procyon A in the Hertzsprung-Russell diagram. For more than 15 years several different groups have studied the solar-like oscillations in Procyon A to determine its evolutionary state. Although several studies independently detected power excess in the periodogram, there is no agreement on the actual oscillation frequencies yet. This is probably due to either insufficient high-quality data (i.e., aliasing) or due to intrinsic properties of the star (i.e., short mode lifetimes). Now a spectroscopic multi-site campaign using 10 telescopes world-wide (minimizing aliasing effects) with a total time span of nearly 4 weeks (increase the frequency resolution) is performed to identify frequencies in this star and finally determine its properties and evolutionary state.
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arxiv:0710.3772
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We solve Grothendieck's localization problem for certain class of rings arising from the tight closure theory. The idea of the proof depends heavily on the study of the relative version of the Frobenius map.
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arxiv:0710.3782
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We employ the hyper central approach to study the masses and magnetic moments of the baryons constituting single charm and beauty quark. The confinement potential is assumed in the hyper central co-ordinates of the coulomb plus power potential form.
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arxiv:0710.3828
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We propose a symmetric version of the multi-scale entanglement renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this Ansatz to find an unknown ground state of a 2D quantum system. Results in the simple 2D quantum Ising model on the $8\times8$ square lattice are found to be very accurate even with the smallest non-trivial truncation parameter.
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arxiv:0710.3829
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We derive a simple consistency relation from the running of the tensor-to-scalar ratio. This new relation is first order in the slow-roll approximation. While for single field models we can obtain what can be found by using other observables, multi-field cases in general give non-trivial contributions dependent on the geometry of the field space and the inflationary dynamics, which can be probed observationally from this relation. The running of the tensor-to-scalar ratio may be detected by direct laser interferometer experiments.
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arxiv:0710.3835
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We demonstrate that the superposition of light polarization states is coherently transferred to electron spins in a semiconductor quantum well. By using time-resolved Kerr rotation we observe the initial phase of Larmor precession of electron spins whose coherence is transferred from light. To break the electron-hole spin entanglement, we utilized the big discrepancy between the transverse g-factors of electrons and light holes. The result encourages us to make a quantum media converter between flying photon qubits and stationary electron spin qubits in semiconductors.
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arxiv:0710.3847
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This is a colloquium-style introduction to two electronic processes in a carbon monolayer (graphene), each having an analogue in relativistic quantum mechanics. Both processes couple electron-like and hole-like states, through the action of either a superconducting pair potential or an electrostatic potential. The first process, Andreev reflection, is the electron-to-hole conversion at the interface with a superconductor. The second process, Klein tunneling, is the tunneling through a p-n junction. Existing and proposed experiments on Josephson junctions and bipolar junctions in graphene are discussed from a unified perspective. CONTENTS: I. INTRODUCTION II. BASIC PHYSICS OF GRAPHENE (Dirac equation; Time reversal symmetry; Boundary conditions; Pseudo-diffusive dynamics) III. ANDREEV REFLECTION (Electron-hole conversion; Retro-reflection vs. specular reflection; Dirac-Bogoliubov-de Gennes equation; Josephson junctions; Further reading) IV. KLEIN TUNNELING (Absence of backscattering; Bipolar junctions; Magnetic field effects; Further reading) V. ANALOGIES (Mapping between NS and p-n junction; Retro-reflection vs. negative refraction; Valley-isospin dependent quantum Hall effect; Pseudo-superconductivity)
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arxiv:0710.3848
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If a normalized K\"{a}hler-Ricci flow $g(t),t\in[0,\infty),$ on a compact K\"{a}hler $n$-manifold, $n\geq 3$, of positive first Chern class satisfies $g(t)\in 2\pi c_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the curvature operator will also uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a K\"{a}hler-Ricci soliton.
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arxiv:0710.3919
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We study some quantum systems described by noncanonical commutation relations formally expressed as [q,p]=ihbar(I + chi H), where H is the associated (harmonic oscillator-like) Hamiltonian of the system, and chi is a Hermitian (constant) operator, i.e. [H,chi]=0 . In passing, we also consider a simple (chi=0 canonical) model, in the framework of a relativistic Klein-Gordon-like wave equation.
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arxiv:0710.3929
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A bound on consecutive clique numbers of graphs is established. This bound is evaluated and shown to often be much better than the bound of the Kruskal-Katona theorem. A bound on non-consecutive clique numbers is also proven.
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arxiv:0710.3960
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A calculation of the deuteron polarization observables $A^d_y$, $A_{yy}$, $A_{xx}$, $A_{xz}$ and the differential cross-section for elastic nucleon-deuteron scattering at incident deuteron energies 270 and 880 MeV in lab is presented. A comparison of the calculations with two different deuteron wave-functions derived from the Bonn-CD $NN$-potential model and the dressed bag quark model is carried out. A model-independent approach, based on an optical potential framework, is used in which a nucleon-nucleon $T$-matrix is assumed to be local and taken on the energy shell, but still depends on the internal nucleon momentum in a deuteron.
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arxiv:0710.4040
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This is an expository paper about the topics listed in the title.
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arxiv:0710.4044
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We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical observables, such as the amplitude, the velocity and the energy of the oscillator grow as power-laws with time. We calculate the associated scaling exponents and we show that their values depend on the asymptotic behaviour of the external potential and on the high frequencies of the noise. Our results are generalized to include dissipative effects and additive noise.
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arxiv:0710.4063
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We study conformational transitions of simple coarse-grained models for protein-like heteropolymers on the simple cubic lattice and off-lattice, respectively, by means of multicanonical sampling algorithms. The effective hydrophobic/polar models do not require the knowledge of the native topology for a given sequence of residues as input. Therefore these models are eligible to investigate general properties of the tertiary folding behaviour of such protein-like heteropolymers.
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arxiv:0710.4095
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We show that one-dimensional Bohmian mechanics is unique, in that, the Bohm trajectories are the only solutions that conserve total left (or right) probability. In Brandt et al., Phys. Lett. A, 249 (1998) 265--270, they define quantile motion--unique trajectories are solved by assuming that the total probability on each side of the particle is conserved. They argue that the quantile trajectories are identical to the Bohm trajectories. Their argument, however, fails to notice the gauge freedom in the definition of the quantum probability current. Our paper sidesteps this under-determinedness of the probability current. The one-dimensional probability conservation can be used for higher dimensional problems if the wave function is separable. Several examples are given using total left probability conservation, most notably, the two-slit experiment.
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arxiv:0710.4099
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Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication (LOCC), in the limit of many copies. While for two pure states a result of Walgate et al. shows that LOCC is just as powerful as global measurements, data hiding states (DiVincenzo et al.) show that locality can impose severe restrictions on the distinguishability of even orthogonal states. Here we determine the optimal error probability and measurement to discriminate many copies of particular data hiding states (extremal d x d Werner states) by a linear programming approach. Surprisingly, the single-copy optimal measurement remains optimal for n copies, in the sense that the best strategy is measuring each copy separately, followed by a simple classical decision rule. We also put a lower bound on the bias with which states can be distinguished by separable operations.
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arxiv:0710.4113
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It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we show that for every diagram of a link in the 3-sphere there exists a diagram of an alternating link in a thickened surface (and an alternating virtual link) with the same Kauffman bracket. We also recover two recent results in the literature relating the Jones and Bollobas-Riordan polynomials and show they arise from two different interpretations of the same embedded graph.
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arxiv:0710.4152
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In this paper we construct random conformal snowflakes with large integral means spectrum at different points. These new estimates are significant improvement over previously known lower bound of the universal spectrum. Our estimates are within 5-10 percent from the conjectured value of the universal spectrum.
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arxiv:0710.4175
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Transport of molecules across membrane channels is investigated theoretically using exactly solvable one-dimensional discrete-state stochastic models. An interaction between molecules and membrane pores is modeled via a set of binding sites with different energies. It is shown that the interaction potential strongly influences the particle currents as well as fluctuations in the number of translocated molecules. For small concentration gradients the attractive sites lead to largest currents and fluctuations, while the repulsive interactions yield the largest fluxes and dispersions for large concentration gradients. Interaction energies that lead to maximal currents and maximal fluctuations are the same only for locally symmetric potentials, while they differ for the locally asymmetric potentials. The conditions for the most optimal translocation transport with maximal current and minimal dispersion are discussed. It is argued that in this case the interaction strength is independent of local symmetry of the potential of mean forces. In addition, the effect of the global asymmetry of the interaction potential is investigated, and it is shown that it also strongly affects the particle translocation dynamics. These phenomena can be explained by analyzing the details of the particle entering and leaving the binding sites in the channel.
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arxiv:0710.4359
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We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of "linear response function" in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process X(s) but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is, if the initial measure is invariant for the given Markov semi-group, then for any pair of times s<t and nice functions f,g, the dissipation, that is, the derivative in s of the covariance of g(X(t)) and f(X(s)) equals the infinitesimal response at time t and direction g to any Markovian perturbation that alters the invariant measure of X(.) in the direction of f at time s. The same applies in the so called FDT regime near equilibrium, i.e. in the limit s going to infinity with t-s fixed, provided X(s) converges in law to an invariant measure for its dynamics. We provide the response function of two generic Markovian perturbations which we then compare and contrast for pure jump processes on a discrete space, for finite dimensional diffusion processes, and for stochastic spin systems.
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arxiv:0710.4394
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We propose a method to obtain physical quantities in the theta vacuum from those at fixed topology, which are different by finite size effects. Extending the work by Brower et al., we derive the formula to estimate these finite size corrections for arbitrary correlators in terms of the topological susceptibility and the theta dependence. Applying this formula, we show that topological susceptibility can be measured through two-point functions of pseudoscalar operator.
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arxiv:0710.4469
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The plan for mass and spin measurement of SUSY particles with the ATLAS detector is presented. The measurements of kinematical distributions, such as edges in the invariant mass of leptons and jets, could be used to constrain the model of SUSY that may be discovered at the LHC. Examples from a few points in the mSUGRA scenario are provided with an emphasis on measurements that can be conducted within the first few years of data taking.
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arxiv:0710.4546
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We present an extensive data set of ~150 localized features from Cassini images of Saturn's Ring A, a third of which are demonstrated to be persistent by their appearance in multiple images, and half of which are resolved well enough to reveal a characteristic "propeller" shape. We interpret these features as the signatures of small moonlets embedded within the ring, with diameters between 40 and 500 meters. The lack of significant brightening at high phase angle indicates that they are likely composed primarily of macroscopic particles, rather than dust. With the exception of two features found exterior to the Encke Gap, these objects are concentrated entirely within three narrow (~1000 km) bands in the mid-A Ring that happen to be free from local disturbances from strong density waves. However, other nearby regions are similarly free of major disturbances but contain no propellers. It is unclear whether these bands are due to specific events in which a parent body or bodies broke up into the current moonlets, or whether a larger initial moonlet population has been sculpted into bands by other ring processes.
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arxiv:0710.4547
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The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a non-commutative ring that is an analog of non-commutative field of two independent variables and prove that the Cremona group embeds in the group of outer automorphisms of this ring. First proof of this result is technical, the second one is conceptual and gives a way to obtain non-commutative rings from the bounded derived categories of coherent sheaves.
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arxiv:0710.4561
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We propose the use of microcanonical analyses for numerical studies of peptide aggregation transitions. Performing multicanonical Monte Carlo simulations of a simple hydrophobic-polar continuum model for interacting heteropolymers of finite length, we find that the microcanonical entropy behaves convex in the transition region, leading to a negative microcanonical specific heat. As this effect is also seen in first-order-like transitions of other finite systems, our results provide clear evidence for recent hints that the characterisation of phase separation in first-order-like transitions of finite systems profits from this microcanonical view.
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arxiv:0710.4575
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We study the behaviour of families of Ricci-flat Kahler metrics on a projective Calabi-Yau manifold when the Kahler classes degenerate to the boundary of the ample cone. We prove that if the limit class is big and nef the Ricci-flat metrics converge smoothly on compact sets outside a subvariety to a limit incomplete Ricci-flat metric. The limit can also be understood from algebraic geometry.
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arxiv:0710.4579
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Demands for implementing original OSs that can achieve high I/O performance on PC/AT compatible hardware have recently been increasing, but conventional OS debugging environments have not been able to simultaneously assure their stability, be easily customized to new OSs and new I/O devices, and assure efficient execution of I/O operations. We therefore developed a novel OS debugging method using a lightweight virtual machine. We evaluated this debugging method experimentally and confirmed that it can transfer data about 5.4 times as fast as the conventional virtual machine monitor.
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arxiv:0710.4635
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On a commercial digital still camera (DSC) controller chip we practice a novel SOC test integration platform, solving real problems in test scheduling, test IO reduction, timing of functional test, scan IO sharing, embedded memory built-in self-test (BIST), etc. The chip has been fabricated and tested successfully by our approach. Test results justify that short test integration cost, short test time, and small area overhead can be achieved. To support SOC testing, a memory BIST compiler and an SOC testing integration system have been developed.
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arxiv:0710.4669
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FPGAs, as computing devices, offer significant speedup over microprocessors. Furthermore, their configurability offers an advantage over traditional ASICs. However, they do not yet enjoy high-level language programmability, as microprocessors do. This has become the main obstacle for their wider acceptance by application designers. ROCCC is a compiler designed to generate circuits from C source code to execute on FPGAs, more specifically on CSoCs. It generates RTL level HDLs from frequently executing kernels in an application. In this paper, we describe ROCCC's system overview and focus on its data path generation. We compare the performance of ROCCC-generated VHDL code with that of Xilinx IPs. The synthesis result shows that ROCCC-generated circuit takes around 2x ~ 3x area and runs at comparable clock rate.
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arxiv:0710.4716
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In this paper, we present power emulation, a novel design paradigm that utilizes hardware acceleration for the purpose of fast power estimation. Power emulation is based on the observation that the functions necessary for power estimation (power model evaluation, aggregation, etc.) can be implemented as hardware circuits. Therefore, we can enhance any given design with "power estimation hardware", map it to a prototyping platform, and exercise it with any given test stimuli to obtain power consumption estimates. Our empirical studies with industrial designs reveal that power emulation can achieve significant speedups (10X to 500X) over state-of-the-art commercial register-transfer level (RTL) power estimation tools.
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arxiv:0710.4742
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Many existing thermal management techniques focus on reducing the overall power consumption of the chip, and do not address location-specific temperature problems referred to as hotspots. We propose the use of dynamic runtime reconfiguration to shift the hotspot-inducing computation periodically and make the thermal profile more uniform. Our analysis shows that dynamic reconfiguration is an effective technique in reducing hotspots for NoCs.
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arxiv:0710.4764
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A new scheme for amplification of coherent gamma rays is proposed. The key elements are crystalline undulators - single crystals with periodically bent crystallographic planes exposed to a high energy beam of charged particles undergoing channeling inside the crystals. The scheme consists of two such crystals separated by a vacuum gap. The beam passes the crystals successively. The particles perform undulator motion inside the crystals following the periodic shape of the crystallographic planes. Gamma rays passing the crystals parallel to the beam get amplified due to interaction with the particles inside the crystals. The term `gamma klystron' is proposed for the scheme because its operational principles are similar to those of the optical klystron. A more simple one-crystal scheme is considered as well for the sake of comparison. It is shown that the gamma ray amplification in the klystron scheme can be reached at considerably lower particle densities than in the one-crystal scheme, provided that the gap between the crystals is sufficiently large.
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arxiv:0710.4772
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The proper motion measurements for 143 previously known L and T dwarfs are presented. From this sample we identify and discuss 8 high velocity L dwarfs. We also find 4 new wide common proper motion binaries/multiple systems. Using the moving cluster methods we have also identified a number of L dwarfs that may be members of the Ursa Major (age ~400 Myr), the Hyades (age ~625 Myr) and the Pleiades (age ~125 Myr) moving groups.
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arxiv:0710.4786
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This paper surveys the characteristics of multimedia systems. Multimedia applications today are dominated by compression and decompression, but multimedia devices must also implement many other functions such as security and file management. We introduce some basic concepts of multimedia algorithms and the larger set of functions that multimedia systems-on-chips must implement.
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arxiv:0710.4821
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This contribution presents a new approach for allocating suitable function-implementation variants depending on given quality-of-service function-requirements for run-time reconfigurable multi-device systems. Our approach adapts methodologies from the domain of knowledge-based systems which can be used for doing run-time hardware/software resource usage optimizations.
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arxiv:0710.4850
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In this partly expository paper we study van der Corput sets in $\Z^d$, with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some classical results obtained for $d=1$ in \cite{K-MF} and \cite{R}, establish new characterizations, introduce and discuss some modifications of van der Corput sets which correspond to various notions of recurrence, provide numerous examples and formulate some natural open questions.
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arxiv:0710.4861
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We study the static correlation functions of the Richardson pairing model (also known as the reduced or discrete-state BCS model) in the canonical ensemble. Making use of the Algebraic Bethe Ansatz formalism, we obtain exact expressions which are easily evaluated numerically for any value of the pairing strength up to large numbers of particles. We provide explicit results at half-filling and extensively discuss their finite-size scaling behavior.
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arxiv:0710.4865
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We present the results of the analysis of an archival observation of LMC X-2 performed with XMM/Newton. The spectra taken by high-precision instruments have never been analyzed before. We find an X-ray position for the source that is inconsistent with the one obtained by ROSAT, but in agreement with the Einstein position and that of the optical counterpart. The correlated spectral and timing behaviour of the source suggests that the source is probably in the normal branch of its X-ray color-color diagram. The spectrum of the source can be fitted with a blackbody with a temperature 1.5 keV plus a disk blackbody at 0.8 keV. Photoelectric absorption from neutral matter has an equivalent hydrogen column of 4 x 10^{20} cm^{-2}. An emission line, which we identify as the O VIII Lyman alpha line, is detected, while no feature due to iron is detected in the spectrum. We argue that the emission of this source can be straightforwardly interpreted as a sum of the emission from a boundary layer between the NS and the disc and a blackbody component coming from the disc itself. Other canonical models that are used to fit Z-sources do not give a satisfactory fit to the data. The detection of the O VIII emission line (and the lack of detection of lines in the iron region) can be due to the fact that the source lies in the Large Magellanic Cloud.
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arxiv:0710.4934
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We interpret the recent gravitational lensing observations of Jee et al. \cite{Jee} as first evidence for a {\it caustic} ring of dark matter in a galaxy cluster. A caustic ring unavoidably forms when a cold collisionless flow falls with net overall rotation in and out of a gravitational potential well. Evidence for caustic rings of dark matter was previously found in the Milky Way and other isolated spiral galaxies. We argue that galaxy clusters have at least one and possibly two or three caustic rings. We calculate the column density profile of a caustic ring in a cluster and show that it is consistent with the observations of Jee et al.
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arxiv:0710.4936
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We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well-separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.
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arxiv:0710.4960
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A new class of twistor string theories were recently constructed by Abou-Zeid, Hull and Mason. The most interesting one of these theories has the particle content of N=8 supergravity. Arguments are given for the vanishing of the (+ - -)-helicity amplitude for gravitons which suggest that this theory describes a chiral N=8 supergravity rather than Einstein supergravity.
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arxiv:0710.4961
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We establish a nonminimal Einstein-Yang-Mills-Higgs model, which contains six coupling parameters. First three parameters relate to the nonminimal coupling of non-Abelian gauge field and gravity field, two parameters describe the so-called derivative nonminimal coupling of scalar multiplet with gravity field, and the sixth parameter introduces the standard coupling of scalar field with Ricci scalar. The formulated six-parameter nonminimal Einstein-Yang-Mills-Higgs model is applied to cosmology. We show that there exists a unique exact cosmological solution of the de Sitter type for a special choice of the coupling parameters. The nonminimally extended Yang-Mills and Higgs equations are satisfied for arbitrary gauge and scalar fields, when the coupling parameters are specifically related to the curvature constant of the isotropic spacetime. Basing on this special exact solution we discuss the problem of a hidden anisotropy of the Yang-Mills field, and give an explicit example, when the nonminimal coupling effectively screens the anisotropy induced by the Yang-Mills field and thus restores the isotropy of the model.
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arxiv:0710.4992
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This paper presents a review of methods for collecting and analysing data on complex activities. Starting with methods developed for design, we examine the possibility to transpose them to other complex activities, especially activities referring to sensorial expertise. R\'esum\'e Ce texte pr\'esente une revue de m\'ethodes pour recueillir et analyser des donn\'ees sur des actvit\'es complexes. A partir de m\'ethodes d\'evelopp\'ees pour des actvit\'es de conception, nous examinons la possibilit\'e de les transposer \`a d'autres actvit\'es complexes, notamment des actvit\'es faisant \`a appel \`a des expertises sensorielles.
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arxiv:0710.4999
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The $s$-$\bar{s}$ asymmetry in nucleon sea is an important observable for understanding nucleon structure and strong interaction. There have been many theoretical attempts on this subject and recently on its relation to the "NuTeV anomaly". Calculations with different theoretical frameworks lead to different conclusions. Here assuming a newly proposed penta-quark configuration for the $s$-$\bar{s}$ asymmetry in nucleon, we examine its contribution to the "NuTeV anomaly", with a result of about $10-20%$.
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arxiv:0710.5032
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High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schr\"{o}dinger equation is cast into nonlinear Riccati equation, which is solved analytically in first iteration of the quasi-linearization method (QLM). The zeroth iteration is based on general features of the exact solution near the boundaries. The approach is illustrated on the Yukawa potential. The results enable accurate analytical estimates of effects of parameter variations on physical systems.
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arxiv:0710.5042
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In this review article we compare the recent work of Peter Lynds, "On a finite universe with no beginning or end", with that of Stephen Hawking, primarily "Quantum Cosmology, M-Theory, and the Anthropic Principle", and two foundational works by Sean M. Carroll and Jennifer Chen, "Does Inflation Provide Natural Conditions for the Universe" and "Spontaneous Inflation and the Origin of the Arrow of Time", in order to evaluate their comparative treatments of the nature and role of causality, time ordering, thermodynamic reversibility, singularities and boundary conditions in the formation of the early universe. We briefly reference Smolin and Kauffman's recent arguments with respect to possible processes of "evolutionary selection" in early universe formation as an alternative explanation to key elements of Hawking's earlier "M-Theory", and its attendant anthropic principle. We also briefly excerpt a short section of Smolin's recent work on topology in quantum loop gravity, simply as an illustrative example of the type of complex quantum topological transformation which he offers as a theoretical alternative to string theory in quantum cosmology.
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arxiv:0710.5046
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We evaluate the quasinormal modes of massless Dirac perturbation in a Schwarzschild black hole surrounded by the free static spherically symmetric quintessence by using the third-order WKB approximation. The result shows that due to the presence of quintessence, the massless field damps more slowly. The real part of the quasinormal modes increases and the the absolute value of the imaginary part increases when the state parameter $w_q$ increases. In other words, the massless Dirac field decays more rapidly for the larger $w_q$. And the peak value of potential barrier gets higher as $|k|$ increases and the location of peak moves along the right for fixed $w_q$.
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arxiv:0710.5064
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We study multipliers of Hardy-Orlicz spaces $\mH_{\Phi}$ which are strictly contained between $\bigcup_{p>0}H^p$ and so-called ``big'' Hardy-Orlicz spaces. Big Hardy-Orlicz spaces, carrying an algebraic structure, are equal to their multiplier algebra, whereas in classical Hardy spaces $H^p$, the multipliers reduce to $H^{\infty}$. For Hardy-Orlicz spaces $\mH_{\Phi}$ between these two extremal situations and subject to some conditions, we exhibit multipliers that are in Hardy-Orlicz spaces the defining functions of which are related to $\Phi$. Even if the results do not entirely characterize the multiplier algebra, some examples show that we are not very far from precise conditions. In certain situations we see how the multiplier algebra grows in a sense from $\Hi$ to big Hardy-Orlicz spaces when we go from classical $H^p$ spaces to big Hardy-Orlicz spaces. However, the multiplier algebras are not always ordered as their underlying Hardy-Orlicz spaces. Such an ordering holds in certain situations, but examples show that there are large Hardy-Orlicz spaces for which the multipliers reduce to $\Hi$ so that the multipliers do in general not conserve the ordering of the underlying Hardy-Orlicz spaces. We apply some of the multiplier results to construct Hardy-Orlicz spaces close to $\bigcup_{p>0}H^p$ and for which the free interpolating sequences are no longer characterized by the Carleson condition which is well known to characterize free interpolating sequences in $H^p$, $p>0$.
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arxiv:0710.5066
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Discussion of ``The William Kruskal Legacy: 1919--2005'' by Stephen E. Fienberg, Stephen M. Stigler and Judith M. Tanur [arXiv:0710.5063]
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arxiv:0710.5079
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Discussion of ``The William Kruskal Legacy: 1919--2005'' by Stephen E. Fienberg, Stephen M. Stigler and Judith M. Tanur [arXiv:0710.5063]
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arxiv:0710.5085
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We show that degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by 35.
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arxiv:0710.5108
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We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Amp\`ere equations. This type of equations is precisely what is needed in order to construct K\"ahler-Einstein metrics over irreducible singular K\"ahler spaces with ample or trivial canonical sheaf and singular K\"ahler-Einstein metrics over varieties of general type.
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arxiv:0710.5109
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The results of a world-wide coordinated observational campaign on the broad-lined Type Ic SN 2003jd are presented. In total, 74 photometric data points and 26 spectra were collected using 11 different telescopes. SN 2003jd is one of the most luminous SN Ic ever observed. A comparison with other Type Ic supernovae (SNe Ic) confirms that SN 2003jd represents an intermediate case between broad-line events (2002ap, 2006aj), and highly energetic SNe (1997ef, 1998bw, 2003dh, 2003lw), with an ejected mass of M_{ej} = 3.0 +/- 1 Mo and a kinetic energy of E_{k}(tot) = 7_{-2}^{+3} 10^{51} erg. SN 2003jd is similar to SN 1998bw in terms of overall luminosity, but it is closer to SNe 2006aj and 2002ap in terms of light-curve shape and spectral evolution. The comparison with other SNe Ic, suggests that the V-band light curves of SNe Ic can be partially homogenized by introducing a time stretch factor. Finally, due to the similarity of SN 2003jd to the SN 2006aj/XRF 060218 event, we discuss the possible connection of SN 2003jd with a GRB.
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arxiv:0710.5173
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We prove a formula, with power savings, for the sixth moment of Dirichlet L-functions averaged over moduli $q$, over primitive characters $\chi$ modulo $q$, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.
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arxiv:0710.5176
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We propose a simple explanation for the increase of approximately 3 MeV/c^2 in the mass value of the X(3872) obtained from D^{*0} {D^0}bar decay relative to that obtained from decay to J/psi pi+ pi-. If the total width of the X(3872) is 2-3 MeV, the peak position in the D^{*0} {D^0}bar invariant mass distribution is sensitive to the final state orbital angular momentum because of the proximity of the X(3872) to D^{*0} {D^0}bar threshold. We show that for total width 3 MeV and one unit of orbital angular momentum, a mass shift ~3 MeV/c^2 is obtained; experimental mass resolution should slightly increase this value. A consequence is that spin-parity 2^- is favored for the X(3872).
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arxiv:0710.5191
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In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an arbitrary metric space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the stationary degree distributions in heterogeneous PA networks. We show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in presence of heterogeneity.
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arxiv:0710.5281
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We give an example of a local normal domain $R$ such that the map of Grothendieck groups $\G(R) \to \G(\hat R)$ is not injective. We also raise some questions about the kernel of that map.
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arxiv:0710.5336
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We explore theoretically the novel superfluidity of harmonically-trapped polarized ultracold fermionic atoms in a two-dimensional (2D) optical lattice by solving the Bogoliubov-de Gennes equations. The pairing amplitude is found to oscillate along the radial direction at low particle density and along the angular direction at high density. The former is consistent with the existing experiments and the latter is a newly predicted Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, which can be tested in experiments.
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arxiv:0710.5484
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We analyze a toy swiss-cheese cosmological model to study the averaging problem. In our model, the cheese is the EdS model and the holes are constructed from a LTB solution. We study the propagation of photons in the swiss-cheese model, and find a phenomenological homogeneous model to describe observables. Following a fitting procedure based on light-cone averages, we find that the the expansion scalar is unaffected by the inhomogeneities. This is because of spherical symmetry. However, the light-cone average of the density as a function of redshift is affected by inhomogeneities. The effect arises because, as the universe evolves, a photon spends more and more time in the (large) voids than in the (thin) high-density structures. The phenomenological homogeneous model describing the light-cone average of the density is similar to the concordance model. Although the sole source in the swiss-cheese model is matter, the phenomenological homogeneous model behaves as if it has a dark-energy component. Finally, we study how the equation of state of the phenomenological model depends on the size of the inhomogeneities, and find that the equation-of-state parameters w_0 and w_a follow a power-law dependence with a scaling exponent equal to unity. That is, the equation of state depends linearly on the distance the photon travels through voids. We conclude that within our toy model, the holes must have a present size of about 250 Mpc to be able to mimic the concordance model.
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arxiv:0710.5505
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Procyon A, a bright F5 IV-V Sun-like star, is justifiably regarded as a prime asteroseismological target. This star was repeatedly observed by MOST, a specialized microsatellite providing long-term, non-interrupted broadband photometry of bright targets. So far, the widely anticipated p modes eluded direct photometric detection, though numerous independent approaches hinted for the presence of signals in the f~0.5-1.5 mHz range. Implementation of an alternative approach in data processing, as well as combination of the MOST data from 2004 and 2005 (264189 measurements in total) helps to reduce the instrumental noise affecting previous reductions, bringing the 3-sigma detection limit down to ~5.5 part-per-million in the f=0.8-1.2 mHz range. This enables to cross-identifiy 16 p-mode frequencies (though not their degrees) which were previously detected via high-precision radial velocity measurements, and provides an estimate of the large spacing, delta_nu =0.0540 mHz at f~1 mHz. The relatively low average amplitude of the detected modes, a=5.8+/-0.6 ppm, closely matches the amplitudes inferred from the ground-based spectroscopy and upper limits projected from WIRE photometry. This also explains why such low-amplitude signals eluded the direct-detection approach which exclusively relied on the MOST 2004 (or 2005) data processed by a standard pipeline.
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arxiv:0710.5531
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We discuss methods for the calculation of disconnected diagrams and their application to various form factors of the nucleon. In particular, we present preliminary results for the strange contribution to the scalar and axial form factors, calculated with N_f=2 dynamical flavors of Wilson fermions on an anisotropic lattice.
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arxiv:0710.5536
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Electron energy-loss spectroscopy (EELS) performed in transmission electron microscopes is shown to directly render the photonic local density of states (LDOS) with unprecedented spatial resolution, currently below the nanometer. Two special cases are discussed in detail: (i) 2D photonic structures with the electrons moving along the translational axis of symmetry and (ii) quasi-planar plasmonic structures under normal incidence. Nanophotonics in general and plasmonics in particular should benefit from these results connecting the unmatched spatial resolution of EELS with its ability to probe basic optical properties like the photonic LDOS.
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arxiv:0710.5553
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We present efficient approximation algorithms for finding Nash equilibria in anonymous games, that is, games in which the players utilities, though different, do not differentiate between other players. Our results pertain to such games with many players but few strategies. We show that any such game has an approximate pure Nash equilibrium, computable in polynomial time, with approximation O(s^2 L), where s is the number of strategies and L is the Lipschitz constant of the utilities. Finally, we show that there is a PTAS for finding an epsilon
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arxiv:0710.5582
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Several recent studies have been devoted to investigating the limitations that ordinary quantum mechanics and/or quantum gravity might impose on the measurability of space-time observables. These analyses are often confined to the simplified context of two-dimensional flat space-time and rely on a simple procedure for the measurement of space-like distances based on the exchange of light signals. We present a generalization of this measurement procedure applicable to all three types of space-time intervals between two events in space-times of any number of dimensions. We also present some preliminary observations on an alternative measurement procedure that can be applied taking into account the gravitational field of the measuring apparatus, and briefly discuss quantum limitations of measurability in this context.
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arxiv:0710.5608
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A new method for the determination of open cluster membership based on a cumulative effect is proposed. In the field of a plate the relative x and y coordinate positions of each star with respect to all the other stars are added. The procedure is carried out for two epochs t_1 and t_2 separately, then one sum is subtracted from another. For a field star the differences in its relative coordinate positions of two epochs will be accumulated. For a cluster star, on the contrary, the changes in relative positions of cluster members at t_1 and t_2 will be very small. On the histogram of sums the cluster stars will gather to the left of the diagram, while the field stars will form a tail to the right. The procedure allows us to efficiently discriminate one group from another. The greater the distance between t_1 and t_2 and the more cluster stars present, the greater is the effect. The accumulation method does not require reference stars, determination of centroids and modelling the distribution of field stars, necessary in traditional methods. By the proposed method 240 open clusters have been processed, including stars up to m<13. The membership probabilities have been calculated and compared to those obtained by the most commonly used Vasilevskis-Sanders method. The similarity of the results acquired the two different approaches is satisfactory for the majority of clusters.
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arxiv:0710.5637
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We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups of Hermitian type give rise to tight totally geodesic maps of Hermitian symmetric spaces. We show that tight maps behave in a functorial way with respect to the Shilov boundary and use this to prove a general structure theorem for tight homomorphisms. Furthermore we classify all tight embeddings of the Poincare' disk.
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arxiv:0710.5641
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The description of the $\eta$ and $\eta^\prime$ mesons in the Dyson-Schwinger approach has relied on the Witten-Veneziano relation. The present paper explores the consequences of using instead its generalization recently proposed by Shore. On the examples of three different model interactions, we find that irrespective of the concrete model dynamics, our Dyson-Schwinger approach is phenomenologically more successful in conjunction with the standard Witten-Veneziano relation than with the proposed generalization valid in all orders in the $1/N_c$ expansion.
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arxiv:0710.5650
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The H-principle, which is the analogue, for CR manifolds, of the classical Hartogs principle in several complex variables, is known to be valid in the small on a pseudoconcave CR manifold of any codimension. However it fails in the large, as has been shown by the counterexample found in [HN1]. Hence there is an underlying obstruction to the global H-principle on a pseudoconcave CR manifold. The purpose of this note is to take the first steps toward a deeper understanding of this obstruction.
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arxiv:0710.5728
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The Cosmic Microwave Background provides our most ancient image of the Universe and our best tool for studying its early evolution. Theories of high energy physics predict the formation of various types of topological defects in the very early universe, including cosmic texture which would generate hot and cold spots in the Cosmic Microwave Background. We show through a Bayesian statistical analysis that the most prominent, 5 degree radius cold spot observed in all-sky images, which is otherwise hard to explain, is compatible with having being caused by a texture. From this model, we constrain the fundamental symmetry breaking energy scale to be phi_0 ~ 8.7 x 10^(15) GeV. If confirmed, this detection of a cosmic defect will probe physics at energies exceeding any conceivable terrestrial experiment.
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arxiv:0710.5737
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Dirac hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with $\gamma=0$. We analyze long distance behaviour of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as $s\to 1$. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with $\beta=0$.
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arxiv:0710.5744
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We study the zeros of the partition function in the complex beta plane (Fisher's zeros) in SU(2) and SU(3) gluodynamics. We discuss their effects on the asymptotic behavior of the perturbative series for the average plaquette. We present new methods to infer the existence of these zeros in region of the complex beta plane where MC reweighting is not reliable. These methods are based on the assumption that the plaquette distribution can be approximated by a phi^4 type distribution. We give new estimates of the locations for a 4^4 lattice. For SU(2), we found zeros at beta =2.18(1) \pm i0.18(2) (which differs from previous estimates), and at beta =2.18(1) \pm i0.22(2). For SU(3), we confirm beta =5.54(2)\pm i0.10(2) and found additional zeros at beta =5.54(2)\pm i0.16(2). Some of the technical material can be found in recent preprints, in the following we emphasize the motivations (why it is important to know the locations of the zeros) and the challenges (why it is difficult to locate the zeros when the volume increases)
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arxiv:0710.5771
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We investigate the effects of unparticles on Compton scattering, e gamma -> e gamma based on a future e^+e^- linear collider such as the CLIC. For different polarization configurations, we calculate the lower limits of the unparticle energy scale Lambda_U for a discovery reach at the center of mass energies sqrt(s)=0.5 TeV- 3 TeV. It is shown that, especially, for smaller values of the mass dimension d, (1 <d <1.3), and for high energies and luminosities of the collider these bounds are very significant. As a stringent limit, we find Lambda_U>80 TeV for d<1.3 at sqrt(s)=3 TeV, and 1 ab^(-1) integrated luminosity per year, which is comparable with the limits calculated from other low and high energy physics implications.
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arxiv:0710.5773
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Let spt(n) denote the total number of appearances of smallest parts in the partitions of n. Recently, Andrews showed how spt(n) is related to the second rank moment, and proved some surprising Ramanujan-type congruences mod 5, 7 and 13. We prove a generalization of these congruences using known relations between rank and crank moments. We obtain explicit Ramanujan-type congruences for spt(n) mod p for p = 11, 17, 19, 29, 31 and 37. Recently, Bringmann and Ono proved that Dyson's rank function has infinitely many Ramanujan-type congruences. Their proof is non-constructive and utilizes the theory of weak Maass forms. We construct two explicit nontrivial examples mod 11 using elementary congruences between rank moments and half-integer weight Hecke eigenforms.
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arxiv:0710.5793
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We study the two-dimensional twisted (0,2) sigma-model on various smooth complex flag manifolds G/B, and explore its relevance to the geometric Langlands program. We find that an equivalence - at the level of the holomorphic chiral algebra - between a bosonic string on G/B and a B-gauged version of itself on G, will imply an isomorphism of classical W-algebras and a level relation which underlie a geometric Langlands correspondence for G=SL(N,C). This furnishes an alternative physical interpretation of the geometric Langlands correspondence for G=SL(N,C), to that demonstrated earlier by Kapustin and Witten via an electric-magnetic duality of four-dimensional gauge theory. Likewise, the Hecke operators and Hecke eigensheaves will have an alternative physical interpretation in terms of the correlation functions of local operators in the holomorphic chiral algebra of a quasi-topological sigma-model without boundaries. A forthcoming paper will investigate the interpretation of a ``quantum'' geometric Langlands correspondence for G=SL(N,C) in a similar setting, albeit with fluxes of the sigma-model moduli which induce a ``quantum'' deformation of the relevant classical algebras turned on.
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arxiv:0710.5796
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The Edelweiss programme is dedicated to the direct search for Dark Matter as massive weakly interacting particles (WIMPs) with Germanium cryogenic detectors operated in the Laboratoire Souterrain de Modane in the French Alps at a depth of 4800 mwe. After the initial phase Edelweiss I, which involved a total mass of 1 kg, the second step of the programme, Edelweiss II, currently operates 9 kg of detectors and an active shielding of 100 m^2 muon veto detectors and is now in its commissioning phase. The current status and performance of the Edelweiss II set-up in terms of backgrounds will be given, the underground muon flux measured with the muon veto system will be presented.
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arxiv:0710.5849
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For real power series whose non-zero coefficients satisfy $|a_m|^{1/m}\to~1$ we prove a stronger version of Fabry theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.
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arxiv:0710.5894
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In almost all of the studies devoted to the time delay and the frequency shift of light, the calculations are based on the integration of the null geodesic equations. However, the above-mentioned effects can be calculated without integrating the geodesic equations if one is able to determine the bifunction $\Omega(x_A, x_B)$ giving half the squared geodesic distance between two points $x_A$ and $x_B$ (this bifunction may be called Synge's world function). In this lecture, $\Omega(x_A, x_B)$ is determined up to the order $1/c^3$ within the framework of the PPN formalism. The case of a stationary gravitational field generated by an isolated, slowly rotating axisymmetric body is studied in detail. The calculation of the time delay and the frequency shift is carried out up to the order $1/c^4$. Explicit formulae are obtained for the contributions of the mass, of the quadrupole moment and of the internal angular momentum when the only post-Newtonian parameters different from zero are $\beta$ and $\gamma$. It is shown that the frequency shift induced by the mass quadrupole moment of the Earth at the order $1/c^3$ will amount to $10^{-16}$ in spatial experiments like the ESA's Atomic Clock Ensemble in Space mission. Other contributions are briefly discussed.
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arxiv:0711.0034
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We have developed a method for depositing graphene monolayers and bilayers with minimum lateral dimensions of 2-10 nm by the mechanical exfoliation of graphite onto the Si(100)-2x1:H surface. Room temperature, ultra-high vacuum (UHV) tunnelling spectroscopy measurements of nanometer-sized single-layer graphene reveal a size dependent energy gap ranging from 0.1-1 eV. Furthermore, the number of graphene layers can be directly determined from scanning tunnelling microscopy (STM) topographic contours. This atomistic study provides an experimental basis for probing the electronic structure of nanometer-sized graphene which can assist the development of graphene-based nanoelectronics.
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arxiv:0711.0050
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We give an explicit description of the (lowering) Kashiwara operators on Mirkovi\'c-Vilonen polytopes in types $B$ and $C$, which provides a simple method for generating Mirkovi\'c-Vilonen polytopes inductively. This description can be thought of as a modification of the original Anderson-Mirkovi\'c conjecture, which Kamnitzer proved in the case of type $A$, and presented a counterexample in the case of type $C_{3}$.
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arxiv:0711.0071
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Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
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arxiv:0711.0086
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Magneto-oscillations in kinetic and magnetic response functions of a few underdoped cuprates are perhaps one of the most striking observations since many probes of underdoped cuprates clearly point to a non Fermi-liquid normal state. Their observation in the vortex state well below the upper critical field raises a doubt concerning their normal state origin. Here I propose an explanation of the magneto-oscillations as emerging from the quantum interference of the vortex lattice and checkerboard modulations of the electron density of states revealed by STM with atomic resolution in some cuprate superconductors. The checkerboard effectively pins the vortex lattice, when the period of the latter is commensurate with the period of the checkerboard. This condition yields 1/\sqrt{B} periodicity of the response functions versus magnetic field B, rather than 1/B periodicity of conventional normal state oscillations. Our solution of the Gross-Pitaevskii-type equation for composed charged bosons accounting for the d-wave symmetry of the order-parameter and its checkerboard modulations describes well changes in resonant frequency of the tunnel-diode oscillator circuit with YBa2Cu4O8 and the oscillatory part of the Hall resistance and magnetic susceptibility in the mixed state of YBa2Cu3O6.5.
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arxiv:0711.0093
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Given an integer $k \geq 2$, we consider the problem of computing the smallest real number $t(k)$ such that for each set $P$ of points in the plane, there exists a $t(k)$-spanner for $P$ that has chromatic number at most $k$. We prove that $t(2) = 3$, $t(3) = 2$, $t(4) = \sqrt{2}$, and give upper and lower bounds on $t(k)$ for $k>4$. We also show that for any $\epsilon >0$, there exists a $(1+\epsilon)t(k)$-spanner for $P$ that has $O(|P|)$ edges and chromatic number at most $k$. Finally, we consider an on-line variant of the problem where the points of $P$ are given one after another, and the color of a point must be assigned at the moment the point is given. In this setting, we prove that $t(2) = 3$, $t(3) = 1+ \sqrt{3}$, $t(4) = 1+ \sqrt{2}$, and give upper and lower bounds on $t(k)$ for $k>4$.
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arxiv:0711.0114
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Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e.g. by cosmic microwave anisotropy probes. A key issue in that theory is to extract the gauge invariant degrees of freedom which allow unambiguous comparison between theory and experiment. When one goes beyond first (linear) order, the task of writing the Einstein equations expanded to n'th order in terms of quantities that are gauge invariant up to terms of higher orders becomes highly non-trivial and cumbersome. This fact has prevented progress for instance on the issue of the stability of linear perturbation theory and is a subject of current debate in the literature. In this series of papers we circumvent these difficulties by passing to a manifestly gauge invariant framework. In other words, we only perturb gauge invariant, i.e. measurable quantities, rather than gauge variant ones. Thus, gauge invariance is preserved non perturbatively while we construct the perturbation theory for the equations of motion for the gauge invariant observables to all orders. In this first paper we develop the general framework which is based on a seminal paper due to Brown and Kuchar as well as the realtional formalism due to Rovelli. In the second, companion, paper we apply our general theory to FRW cosmologies and derive the deviations from the standard treatment in linear order. As it turns out, these deviations are negligible in the late universe, thus our theory is in agreement with the standard treatment. However, the real strength of our formalism is that it admits a straightforward and unambiguous, gauge invariant generalisation to higher orders. This will also allow us to settle the stability issue in a future publication.
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arxiv:0711.0115
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Anisotropic flows ($v_1$, $v_2$, $v_3$ and $v_4$) of light fragments up till the mass number 4 as a function of rapidity have been studied for 25 MeV/nucleon $^{40}$Ca + $^{40}$Ca at large impact parameters by Quantum Molecular Dynamics model. A phenomenological scaling behavior of rapidity dependent flow parameters $v_n$ (n = 1, 2, 3 and 4) has been found as a function of mass number plus a constant term, which may arise from the interplay of collective and random motions. In addition, $v_4/{v_2}^2$ keeps almost independent of rapidity and remains a rough constant of 1/2 for all light fragments.
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arxiv:0711.0127
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Discrete dynamical systems defined on the state space {0,1,...,p-1}^n have been used in multiple applications, most recently for the modeling of gene and protein networks. In this paper we study to what extent well-known theorems by Smale and Hirsch, which form part of the theory of (continuous) monotone dynamical systems, generalize or fail to do so in the discrete case. We show that that arbitrary m-dimensional systems cannot necessarily be embedded into n-dimensional cooperative systems for n=m+1, as in the Smale theorem for the continuous case, but we show that this is possible for n=m+2 as long as p is sufficiently large. We also prove that a natural discrete analogue of strong cooperativity implies nontrivial bounds on the lengths of periodic orbits and imposes a condition akin to Lyapunov stability on all attractors. Finally, we explore several natural candidates for definitions of irreducibility of a discrete system. While some of these notions imply the strong cooperativity of a given cooperative system and impose even tighter bounds on the lengths of periodic orbits than strong cooperativity alone, other plausible definitions allow the existence of exponentially long periodic orbits.
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arxiv:0711.0138
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Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S^5 superstring world-sheet theory in terms of physical degrees of freedom we construct the Pohlmeyer-reduced version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. Its small-fluctuation spectrum contains 8 bosonic and 8 fermionic degrees of freedom with equal masses. We conjecture that the reduced model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS_2 x S^2 superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.
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arxiv:0711.0155
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Optimal sample path properties of stochastic processes often involve generalized H\"{o}lder- or variation norms. Following a classical result of Taylor, the exact variation of Brownian motion is measured in terms of $\psi (x) \equiv $ $x^{2}/\log \log (1/x) $ near $0+$. Such $\psi $-variation results extend to classes of processes with values in abstract metric spaces. (No Gaussian or Markovian properties are assumed.) To establish integrability properties of the $\psi $-variation we turn to a large class of Gaussian rough paths (e.g. Brownian motion and L\'{e}vy's area viewed as a process in a Lie group) and prove Gaussian integrability properties using Borell's inequality on abstract Wiener spaces. The interest in such results is that they are compatible with rough path theory and yield certain sharp regularity and integrability properties (for iterated Stratonovich integrals, for example) which would be difficult to obtain otherwise. At last, $\psi $-variation is identified as robust regularity property of solutions to (random) rough differential equations beyond semimartingales.
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arxiv:0711.0163
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A classical problem in analytic number theory is to study the distribution of $\alpha p$ modulo 1, where $\alpha$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p+2$ is an almost-prime (the existence of infinitely many such $p$ is another topical result in prime number theory) and prove that its distribution has a similar property.
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arxiv:0711.0171
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Tube formulas (by which we mean an explicit formula for the volume of an $\epsilon$-neighbourhood of a subset of a suitable metric space) have been used in many situations to study properties of the subset. For smooth submanifolds of Euclidean space, this includes Weyl's celebrated results on spectral asymptotics, and the subsequent relation between curvature and spectrum. Additionally, a tube formula contains information about the dimension and measurability of rough sets. In convex geometry, the tube formula of a convex subset of Euclidean space allows for the definition of certain curvature measures. These measures describe the curvature of sets which are not too irregular to support derivatives. In this survey paper, we describe some recent advances in the development of tube formulas for self-similar fractals, and their applications and connections to the other topics mentioned here.
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arxiv:0711.0173
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We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.
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arxiv:0711.0224
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We study hadronization of the final state in a particle-antiparticle annihilation using a holographic gravity dual description of QCD. At the point of hadronization we match the events to a simple (Gaussian) energy distribution in the five dimensional theory. The final state multiplicities are then modelled by calculating the overlap between the Gaussian and a set of functions in the fifth dimension which represent each hadron. We compare our results to those measured in e+e- collisions at LEP and PEP-PETRA. Hadron production numbers, which differ in range by four orders of magnitude, are reproduced to well within a factor of two.
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arxiv:0711.0300
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The spatial distribution of the cosmic-ray flux is important in understanding the Interstellar Medium (ISM) of the Galaxy. This distribution can be analyzed by studying different molecular species along different sight lines whose abundances are sensitive to the cosmic-ray ionization rate. Recently several groups have reported an enhanced cosmic-ray ionization rate in diffuse clouds compared to the standard value, zeta(average)=2.5e-17 s^-1, measured toward dense molecular clouds. In an earlier work we reported an enhancement in the cosmic ray rate of 20 towards HD185418. McCall et al. have reported enhancements of 48 towards zeta Persei based on the observed abundance of H$_{3}^+ while Le Petit et al. found a cosmic ray enhancement of ~10 to be consistent with their models for this same sight line. Here we revisit zeta Persei and perform a detailed calculation using a self-consistent treatment of the hydrogen chemistry, grain physics, energy and ionization balance, and excitation physics. We show that the value of zeta deduced from the H$_{3}^+$ column density in the diffuse region of the sightline depends strongly on the properties of the grains because they remove free electrons and change the hydrogen chemistry. The observations are largely consistent with a cosmic ray enhancement of 40, with several diagnostics indicating higher values. This underscores the importance of a full treatment of grain physics in studies of interstellar chemistry.
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arxiv:0711.0335
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We develop a simple method of dark energy reconstruction using a geometrical form of the luminosity-distance relation. In this method the FRW dynamical system with dark energy is reconstructed instead of the equation of state parameter. We give several examples which illustrate the usefulness of our method in fitting the redshift transition from the decelerating to accelerating phase as the value of the Hubble function at the transition.
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arxiv:0711.0359
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Nuclear parton distributions and structure functions are determined in an effective chiral quark theory. We also discuss an extension of our model to fragmentation functions.
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arxiv:0711.0389
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