Related papers: Berry-Robnik level statistics in a smooth billiard…
New Berry--Esseen-type bounds, with explicit constant factors, for the distribution of the Student statistic and, equivalently, for that of the self-normalized sum of independent zero-mean random variables are obtained. These bounds are…
It has been recently found that the equations of motion of several semiclassical systems must take into account anomalous velocity terms arising from Berry phase contributions. Those terms are for instance responsible for the spin Hall…
We propose a general framework for statistical inference on the overall strengths of players in pairwise comparisons, allowing for potential shifts in the covariate distribution. These covariates capture important contextual information…
Polygonalization of any smooth billiard boundary can be carried out in several ways. We show here that the semiclassical description depends on the polygonalization process and the results can be inequivalent. We also establish that…
We suggest that random matrix theory applied to a classical action matrix can be used in classical physics to distinguish chaotic from non-chaotic behavior. We consider the 2-D stadium billiard system as well as the 2-D anharmonic and…
Quantum ergodicity of classically chaotic systems has been studied extensively both theoretically and experimentally, in mathematics, and in physics. Despite this long tradition we are able to present a new rigorous result using only…
The propagation of electromagnetic waves in unmagnetized periodic plasma media is studied using the semiclassical wave packet approximation. The formalism gives rise to Berry effect terms in the equation of motion. The Berry effect…
We examine deviations from Boltzmann-Gibbs statistics for partially equilibrated systems of finite size. We find that such systems are characterized by the Levy distribution whose non-extensivity parameter is related to the number of…
We define a new class of plane billiards - the `pensive billiard' - in which the billiard ball travels along the boundary for some distance depending on the incidence angle before reflecting, while preserving the billiard rule of equality…
We study the classical and quantum ergodic lemon billiard introduced by Heller and Tomsovic in Phys. Today 46(7), 38 (1993), for the case $B=1/2$, which is a classically ergodic system (without a rigorous proof) exhibiting strong stickiness…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…
We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index…
We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random…
In this paper we study scattering of two-dimensional massless Dirac fermions by a potential that depends on a single Cartesian variable. Depending on the energy of the incoming particle and its angle of incidence, there are three different…
The paper establishes the property of splittability of billiard boundary sequences in n dimensional cube into subsequences of fractional parts. This reveals a new property of integrable and weak perturbated Hamilton systems: under a simple…
We present an efficient method to solve Schr\"odinger's equation for perturbations of low rank. In particular, the method allows to calculate the level counting function with very little numerical effort. To illustrate the power of the…
The classification of universality classes of random-matrix theory has recently been extended beyond the Wigner-Dyson ensembles. Several of the novel ensembles can be discussed naturally in the context of superconducting-normal hybrid…
We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
Quantum walks are at present an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior.…