Related papers: Random matrix description of dynamically backscatt…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of…
The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of…
We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…
A new method of path averaging for waves propagating in a random dilute system of identical scatterers is developed. The scattering matrix of such a system is calculated. The method systematically takes into account repeating scatterings on…
We investigate the eigenstructure of matrix formulations used for modeling scattering processes within materials in transmission electron microscopy. Dynamical scattering is crucial for describing the interaction between an electron wave…
In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…
Compton scattering of twisted photons is investigated within a non-relativistic framework using first-order perturbation theory. We formulate the problem in the density matrix theory, which enables one to gain new insights into scattering…
We show in random matrix theory, microwave measurements, and computer simulations that the mean free path of a random medium and the strength and position of an embedded reflector can be determined from radiation scattered by the system.…
Interference of randomly scattered classical waves naturally leads to familiar speckle patterns, where the wave intensity follows an exponential distribution while the wave field itself is described by a circularly symmetric complex normal…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…
Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…
The propagation of light in a resonant atomic vapor can \textit{a priori} be thought of as a multiple scattering process, in which each scattering event redistributes both the direction and the frequency of the photons. Particularly, the…
To what extent can particulate random media be characterised using direct wave backscattering from a single receiver/source? Here, in a two dimensional setting, we show using a machine learning approach that both the particle radius and…
Wave velocity is a key parameter for imaging complex media, but in vivo measurements are typically limited to reflection geometries, where only backscattered waves from short-scale heterogeneities are accessible. As a result, conventional…
Motivated by current interest in understanding statistical properties of random landscapes in high-dimensional spaces, we consider a model of the landscape in $\mathbb{R}^N$ obtained by superimposing $M>N$ plane waves of random wavevectors…
As light travels through a disordered medium such as biological tissues, it undergoes multiple scattering events. This phenomenon is detrimental to in-depth optical microscopy, as it causes a drastic degradation of contrast, resolution and…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
Coherent backscattering is a multiple scattering interference effect which enhances the diffuse reflection off a disordered sample in the backward direction. Classically, the enhanced intensity is twice the average background under well…