23,015 research outputs found
Density-functional theory for fermions in the unitary regime
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 . We use a simple density functional parametrized by an effective
mass and the universal constant , and employ Kohn-Sham density-functional
theory to obtain the parameters from fit to one exactly solvable two-body
problem. This yields 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
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
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
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
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
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
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
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
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
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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