15,648 research outputs found
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
A Universal Interacting Crossover Regime in Two-Dimensional Quantum Dots
Interacting electrons in quantum dots with large Thouless number in the
three classical random matrix symmetry classes are well-understood. When a
specific type of spin-orbit coupling known to be dominant in two dimensional
semiconductor quantum dots is introduced, we show that a new interacting
quantum critical crossover energy scale emerges and low-energy quasiparticles
generically have a decay width proportional to their energy. The low-energy
physics of this system is an example of a universal interacting crossover
regime.Comment: 4 pages, 1 figur
Weak Measurements with Arbitrary Pointer States
The exact conditions on valid pointer states for weak measurements are
derived. It is demonstrated that weak measurements can be performed with any
pointer state with vanishing probability current density. This condition is
found both for weak measurements of noncommuting observables and for -number
observables. In addition, the interaction between pointer and object must be
sufficiently weak. There is no restriction on the purity of the pointer state.
For example, a thermal pointer state is fully valid.Comment: 4 page
Does dynamics reflect topology in directed networks?
We present and analyze a topologically induced transition from ordered,
synchronized to disordered dynamics in directed networks of oscillators. The
analysis reveals where in the space of networks this transition occurs and its
underlying mechanisms. If disordered, the dynamics of the units is precisely
determined by the topology of the network and thus characteristic for it. We
develop a method to predict the disordered dynamics from topology. The results
suggest a new route towards understanding how the precise dynamics of the units
of a directed network may encode information about its topology.Comment: 7 pages, 4 figures, Europhysics Letters, accepte
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
Phenomenological model for symmetry breaking in chaotic system
We assume that the energy spectrum of a chaotic system undergoing symmetry
breaking transitions can be represented as a superposition of independent level
sequences, one increasing on the expense of the others. The relation between
the fractional level densities of the sequences and the symmetry breaking
interaction is deduced by comparing the asymptotic expression of the
level-number variance with the corresponding expression obtained using the
perturbation theory. This relation is supported by a comparison with previous
numerical calculations. The predictions of the model for the
nearest-neighbor-spacing distribution and the spectral rigidity are in
agreement with the results of an acoustic resonance experiment.Comment: accepted for publication in Physical Review
Superstatistical random-matrix-theory approach to transition intensities in mixed systems
We study the fluctuation properties of transition intensities applying a
recently proposed generalization of the random matrix theory, which is based on
Beck and Cohen's superstatistics. We obtain an analytic expression for the
distribution of the reduced transition probabilities that applies to systems
undergoing a transition out of chaos. The obtained distribution fits the
results of a previous nuclear shell model calculations for some electromagnetic
transitions that deviate from the Porter-Thomas distribution. It agrees with
the experimental reduced transition probabilities for the 26A nucleus better
than the commonly used chi-squared distribution.Comment: 14 pages, 3 figure
Gap probabilities in non-Hermitian random matrix theory
We compute the gap probability that a circle of
radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the Ginibre ensembles and their chiral complex counterparts, with both complex (beta=2) or quaternion real (beta=4) matrix elements. For general non-Gaussian weights we give a Fredholm determinant or Pfaffian representation respectively, depending on the non-Hermiticity parameter. At maximal non-Hermiticity, that is for rotationally invariant weights, the product of Fredholm eigenvalues for beta=4 follows from beta=2 by skipping every second factor, in contrast to the known relation for Hermitian ensembles. On additionally choosing Gaussian weights we give new explicit expressions for the Fredholm eigenvalues in the chiral case, in terms of Bessel-K and incomplete Bessel-I functions. This compares to known results for the Ginibre ensembles in terms of incomplete exponentials. Furthermore we present an asymptotic expansion of the logarithm of the gap probability for large argument r at large N in all four ensembles, up to including the third order linear term. We can provide strict upper and lower bounds and present numerical evidence for its conjectured values, depending on the number of exact zero eigenvalues in the chiral ensembles. For the Ginibre ensemble at beta=2 exact results were previously derived by Forrester
Painlev\'e V and time dependent Jacobi polynomials
In this paper we study the simplest deformation on a sequence of orthogonal
polynomials, namely, replacing the original (or reference) weight
defined on an interval by It is a well-known fact that under
such a deformation the recurrence coefficients denoted as and
evolve in according to the Toda equations, giving rise to the
time dependent orthogonal polynomials, using Sogo's terminology. The resulting
"time-dependent" Jacobi polynomials satisfy a linear second order ode. We will
show that the coefficients of this ode are intimately related to a particular
Painlev\'e V. In addition, we show that the coefficient of of the
monic orthogonal polynomials associated with the "time-dependent" Jacobi
weight, satisfies, up to a translation in the Jimbo-Miwa -form of
the same while a recurrence coefficient is up to a
translation in and a linear fractional transformation
These results are found
from combining a pair of non-linear difference equations and a pair of Toda
equations. This will in turn allow us to show that a certain Fredholm
determinant related to a class of Toeplitz plus Hankel operators has a
connection to a Painlev\'e equation
Matrix models and QCD with chemical potential
The Random Matrix Model approach to Quantum Chromodynamics (QCD) with non-vanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral Perturbation Theory (echPT). Two types of Matrix Model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with echPT. All known analytic results for the spectrum of complex and symplectic Matrix Models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent Lattice simulations are also discussed
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