Related papers: Self-averaging of Wigner transforms in random medi…
We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…
Irreversible processes of one-dimensional quantum perfect Lorentz gas is studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouville-von Neumann…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…
We investigate non-classical effects such as fractional revivals, squeezing and higher-order squeezing of photon-added coherent states propagating through a Kerr-like medium.The Wigner functions corresponding to these states at the instants…
We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…
We study a class of self-repelling diffusions on compact Riemannian manifolds whose drift is the gradient of a potential accumulated along their trajectory. When the interaction potential admits a suitable spectral decomposition, the…
We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…
A system of coupled kinetic transport equations for the Wigner distributions of a free variable mass Klein-Gordon field is derived. This set of equations is formally equivalent to the full wave equation for electromagnetic waves in…
We consider the joint distribution of eigenvalue clusters of the Wigner ensemble separated by macroscopic distances (i.e., on the same scale as the difference between the edges of the semicircle law). We prove that under an averaging…
A class of signed joint probability measures for n arbitrary quantum observables is derived and studied based on quasi-characteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner…
In this paper we study the asymptotic phase space energy distribution of solution of the Schr\"{o}dinger equation with a time-dependent random potential. The random potential is assumed to be with slowly decaying correlations. We show that…
We present an analysis of enhanced wave transmission through random media with mirror symmetry about a reflecting barrier. The mathematical model is the acoustic wave equation and we consider two setups, where the wave propagation is along…
We prove that a normalized sequence of multiple Wigner integrals (in a fixed order of free Wigner chaos) converges in law to the standard semicircular distribution if and only if the corresponding sequence of fourth moments converges to 2,…
We derive the joint asymptotic distribution of the outlier eigenvalues of an additively deformed Wigner matrix $H$. Our only assumptions on the deformation are that its rank be fixed and its norm bounded. Our results extend those of [The…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
The study of quenched random systems is facilitated by the idea that the ensemble averages describe the thermal averages for any specific realization of the couplings, provided the system is large enough. Careful examination suggests that…
We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function probability distribution P(w) = (1/V) int…
In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in…
Metaplectic Wigner distributions generalize the most popular time-frequency representations, such as the short-time Fourier transform (STFT) and $\tau$-Wigner distributions, using metaplectic operators. However, in order for a metaplectic…