Related papers: Saturation of number variance in embedded random m…
In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of…
We investigate the problem of effusion of particles initially confined in a finite one-dimensional box of size $L$. We study both passive as well active scenarios, involving non-interacting diffusive particles and run-and-tumble particles,…
Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulae for the microcanonical partition functions in the case of non-interacting massless neutral particles…
Fluctuations play a central role in many fields of physics, from quantum electrodynamics to statistical mechanics. In active matter physics, most models focus on thermal fluctuations due to a surrounding solvent. An alternative but much…
Statistical properties of cross sections are studied for an open system of interacting fermions. The description is based on the effective non-Hermitian Hamiltonian that accounts for the existence of open decay channels preserving the…
Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved,…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
The fluctuations and correlations of matrix elements of cross sections are investigated in open systems that are chaotic in the classical limit. The form of the correlation functions is discussed within a statistical analysis and tested in…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…
We study the effect of gradual symmetry breaking in a non-integrable system on the level fluctuation statistics. We consider the case when the symmetry is represented by a quantum number that takes one of two possible values, so that the…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We experimentally study a gas of $N = 8$ one-dimensional Brownian particles, each confined in a harmonic trap with identical stiffness. The stiffness switches simultaneously between two values at random Poissonian times. This collective…
In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
We investigate the properties of sparse matrix ensembles with particular regard for the spectral ergodicity hypothesis, which claims the identity of ensemble and spectral averages of spectral correlators. An apparent violation of the…
The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings,…
We study numerically the correlations and the distribution of intervals between successive zeros in the fluctuating geometry of stochastic interfaces, described by the Edwards-Wilkinson equation. For equilibrium states we find that the…