Related papers: Random matrices associated with general barrier bi…
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic…
An elliptic random matrix $X$ is a square matrix whose $(i,j)$-entry $X_{ij}$ is independent of the rest of the entries except possibly $X_{ji}$. Elliptic random matrices generalize Wigner matrices and non-Hermitian random matrices with…
We argue that the random-matrix like energy spectra found in pseudointegrable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system. It is shown that the behavior of the…
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal…
We discuss the properties of eigenphases of S--matrices in random models simulating classically chaotic scattering. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are…
We consider a random billiard map, the one in which the standard specular reflection rule is replaced by a random reflection given by a Markov operator. We exhibit an invariant measure for random billiards on general tables. In the special…
We develop an analytical framework and numerical approach to obtain the coefficient of self-diffusivity for the transport of a rarefied gas in channels in the limit of large Knudsen number. This framework provides a method for determining…
It is shown that, for a Hamiltonian with a band structure, the half width of local spectral density of states, or strength function, is closely related to the width of the nonperturbative (NPT) parts of energy eigenfunctions. In the…
We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found…
Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher dimensional distributions to those targeting lower dimensional ones. This leads to a quasi-telescoping property of…
The conductance through open quantum dots or quantum billiards shows fluctuations, that can be explained as interference between waves following different paths between the leads of the billiard. We examine such systems by the use of a…
The Wigner function is a phase space quasi-probability distribution whose negative regions provide a direct, local signature of nonclassicality. To identify where phase-sensitive structure concentrates, we introduce local positive- and…
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
We introduce and study several random combinatorial billiard trajectories. Such a system, which depends on a fixed parameter $p\in(0,1)$, models a beam of light that travels in a Euclidean space, occasionally randomly reflecting off of a…
For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the…
In this work we study the eigenstates and the energy spectra of a generic billiard system with the use of microwave resonators. This is possible due to the exact correspondence between the Schroedinger equation and the electric field…