Related papers: Probability Distribution for Coherent Transport of…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
We consider two different stationary random processes whose probability distributions are very close and indistinguishable by standard tests for large but limited statistics. Yet we demonstrate that these processes can be reliably…
We present theoretical calculations of the ensemble-averaged (a.k.a. effective or coherent) wavefield propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that…
The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
We show in microwave measurements and computer simulations that the contribution of each eigenchannel of the transmission matrix to the density of states (DOS) is the derivative with angular frequency of a composite phase shift. The…
We present a numerical study on the light transport properties and statistics of transmission channels in random media with inhomogeneous disorder. For the case of longitudinal inhomogeneity of disorder we find that the statistics of the…
We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its…
Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are…
Looking at rational solid-fluid mixture theories in the context of their biomechanical perspectives, this work aims at proposing a two-scale constitutive theory of a poroelastic solid infused with an inviscid compressible fluid. The…
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…
A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized…
The transfer of information from one part of a quantum system to another is fundamental to the understanding and design of quantum information processing devices. In the realm of discrete systems such as spin chains, inhomogeneous networks…
The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered…
We discuss "the plane wave approximation" to quantum mechanical scattering using simple one-dimensional examples. The central points of the paper are that (a) plane waves should be thought of as infinitely wide wave packets, and (b) the…
We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave…
We study monochromatic random waves on $\mathbb{R}^n$ defined by Gaussian variables whose variances tend to zero sufficiently fast. This has the effect that the Fourier transform of the monochromatic wave is an absolutely continuous measure…
A theoretical analysis of the statistical distributions of the reflected intensities from random media is presented. We use random matrix theory to analytically deduce the probability densities in the localization regime. Numerical…
We present a self-consistent theory for sound propagation in a simple model of a disordered solid. The solid is modeled as a collection of randomly distributed particles connected by harmonic springs with strengths that depend on the…
The correspondence principle states that the quantum system will approach to the classical system in high quantum numbers. Indeed, the average of the probability density distribution reflects a classical-like distribution. However, the…