22,719 research outputs found

    Density-functional theory for fermions in the unitary regime

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    In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the free Fermi gas with a proportionality constant ξ\xi. We use a simple density functional parametrized by an effective mass and the universal constant ξ\xi, and employ Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields ξ=0.42\xi=0.42 and a rather large effective mass. Our approach is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.Comment: 5 pages, 2 figure

    Probability density of determinants of random matrices

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    In this brief paper the probability density of a random real, complex and quaternion determinant is rederived using singular values. The behaviour of suitably rescaled random determinants is studied in the limit of infinite order of the matrices

    Accuracy and range of validity of the Wigner surmise for mixed symmetry classes in random matrix theory

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    Schierenberg et al. [Phys. Rev. E 85, 061130 (2012)] recently applied the Wigner surmise, i.e., substitution of \infty \times \infty matrices by their 2 \times 2 counterparts for the computation of level spacing distributions, to random matrix ensembles in transition between two universality classes. I examine the accuracy and the range of validity of the surmise for the crossover between the Gaussian orthogonal and unitary ensembles by contrasting them with the large-N results that I evaluated using the Nystrom-type method for the Fredholm determinant. The surmised expression at the best-fitting parameter provides a good approximation for 0 \lesssim s \lesssim 2, i.e., the validity range of the original surmise.Comment: 3 pages in REVTeX, 10 figures. (v2) Title changed, version to appear in Phys. Rev.

    Calculation of some determinants using the s-shifted factorial

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    Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

    Glassy dynamics in granular compaction

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    Two models are presented to study the influence of slow dynamics on granular compaction. It is found in both cases that high values of packing fraction are achieved only by the slow relaxation of cooperative structures. Ongoing work to study the full implications of these results is discussed.Comment: 12 pages, 9 figures; accepted in J. Phys: Condensed Matter, proceedings of the Trieste workshop on 'Unifying concepts in glass physics

    Modelling highway-traffic headway distributions using superstatistics

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    We study traffic clearance distributions (i.e., the instantaneous gap between successive vehicles) and time headway distributions by applying Beck and Cohen's superstatistics. We model the transition from free phase to congested phase with the increase of vehicle density as a transition from the Poisson statistics to that of the random matrix theory. We derive an analytic expression for the spacing distributions that interpolates from the Poisson distribution and Wigner's surmise and apply it to the distributions of the nett distance and time gaps among the succeeding cars at different densities of traffic flow. The obtained distribution fits the experimental results for single-vehicle data of the Dutch freeway A9 and the German freeway A5.Comment: 10 pages, 2 figure

    Full counting statistics of chaotic cavities with many open channels

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    Explicit formulas are obtained for all moments and for all cumulants of the electric current through a quantum chaotic cavity attached to two ideal leads, thus providing the full counting statistics for this type of system. The approach is based on random matrix theory, and is valid in the limit when both leads have many open channels. For an arbitrary number of open channels we present the third cumulant and an example of non-linear statistics.Comment: 4 pages, no figures; v2-added references; typos correcte

    Chaotic quantum dots with strongly correlated electrons

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    Quantum dots pose a problem where one must confront three obstacles: randomness, interactions and finite size. Yet it is this confluence that allows one to make some theoretical advances by invoking three theoretical tools: Random Matrix theory (RMT), the Renormalization Group (RG) and the 1/N expansion. Here the reader is introduced to these techniques and shown how they may be combined to answer a set of questions pertaining to quantum dotsComment: latex file 16 pages 8 figures, to appear in Reviews of Modern Physic

    Anderson localisation in tight-binding models with flat bands

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    We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands that are dispersionless throughout the Brillouin zone. We show that states derived from these flat bands are generically critical in the presence of weak disorder, being neither Anderson localised nor spatially extended. Further, we establish a mapping between this localisation problem and the one of resonances in random impedance networks, which previous work has suggested are also critical. Our conclusions are illustrated using numerical results for a two-dimensional lattice, known as the square lattice with crossings or the planar pyrochlore lattice.Comment: 5 pages, 3 figures, as published (this version includes minor corrections

    Enumeration of RNA structures by Matrix Models

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    We enumerate the number of RNA contact structures according to their genus, i.e. the topological character of their pseudoknots. By using a recently proposed matrix model formulation for the RNA folding problem, we obtain exact results for the simple case of an RNA molecule with an infinitely flexible backbone, in which any arbitrary pair of bases is allowed. We analyze the distribution of the genus of pseudoknots as a function of the total number of nucleotides along the phosphate-sugar backbone.Comment: RevTeX, 4 pages, 2 figure
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