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The coherent process of particle deflection by aligned atomic strings and planes of oriented crystals is accompanied by incoherent scattering by atomic cores. While the coherent particle deflection, described by the axial or planar averaged…

Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability…

An integro-differential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random…

Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral…

We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and…

A numerical-analytical simulation of scattering by a three-barrier heterostructure of an electronic Gaussian wave packet, the spectral width of which is on the order of the distance between the levels of the doublet of quasi-stationary…

In this paper, we consider the reflection and transmission problem of waves by a rapidly oscillating rough interface that exhibits general mixing properties. Using an asymptotic analysis based on a separation of scales, corresponding to a…

We compare two different models of transport of light in a disordered system with a spherical Gaussian distribution of scatterers. A coupled dipole model, keeping into account all interference effects, is compared to an incoherent model,…

The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…

We present a general formalism describing a propagation of an arbitrary multiparticle wave packet in a one-dimensional multimode chiral channel coupled to an ensemble of emitters which are distributed at arbitrary positions. The formalism…

The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant…

By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained.…

The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are…

We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises--Fisher, the Watson and the angular Gaussian families. In addition to several special results we…

Propagation of gamma-beam in the anisotropic medium is considered. The simpliest example of such a medium of the general type is a combination of the two linearly polarized monochromatic laser waves with different frequencies (dichromatic…

Light propagation through turbulence produces speckles, whose ensemble behavior is typically characterized by snapshot intensity statistics. Here, we track the spatiotemporal evolution of individual speckles and quantify fragmentation,…

We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…

We study stationary solutions to the continuity equation for weakly compressible flows. These describe non-equilibrium steady states of weakly dissipative dynamical systems. Compressibility is a singular perturbation that changes the steady…

In various situations where wave transport is preeminent, like in wireless communication, a strong established transmission is present in a complex scattering environment. We develop a novel approach to describe emerging fluctuations, which…