Related papers: Eigenfunction distribution for the Rosenzweig-Port…
In this work we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in…
Diffusion of electrons in a two-dimensional system in static random magnetic fields is studied by solving the time-dependent Schr\"{o}dinger equation numerically. The asymptotic behaviors of the second moment of the wave packets and the…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…
Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of…
The theory of self-reciprocal functions is applied to the study Mordell type integrals. We find two particular eigenfunctions of the double cosine Fourier transform and then use them to evaluate certain one- and two-dimensional Mordell type…
We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the non-orthogonality of resonance…
We consider the {\it fractal von Neumann entropy} associated with the {\it fractal distribution function} and we obtain for some {\it universal classes h of fractons} their entropies. We obtain also for each of these classes a {\it…
The distribution function of local amplitudes of single-particle states in disordered conductors is calculated on the basis of the supersymmetric $\sigma$-model approach using a saddle-point solution of its reduced version. Although the…
For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and…
Mutual space-frequency distribution is proposed and it is shown that Wigner and Weyl distribution functions are only particular cases of these distribution. Mutual distribution for Gaussian signal is analytically obtained. The simple…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…
For energy eigenfunctions of 1-dimensional tight binding model, the distribution of ratio of their nearest components, denoted by f(p), gives information for their fluctuation properties. The shape of f(p) is studied numerically for three…
We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of…
We discuss skewed parton distributions in the coordinate space. Solution of the corresponding LO evolution equation is constructed in terms of eigenfunctions of the evolution kernel and its relation to the conformal symmetry is explained.
Eigenvalue distributions are important dynamical quantities in matrix models, and it is a challenging problem to derive them in tensor models. In this paper, we consider real symmetric order-three tensors with Gaussian distributions as the…
We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger…
The definitions and applications of Radial Distribution Function (RDF) and Structure Factor (SF) to study properties of aggregate are found in many papers and books. The approach adopted to calculate the RDF and the SF to determine the…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…