Generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of scatterers

We presesent an exact generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of identical spherical scatterers. The Foldy-Lax formula yields an expression for the self-energy valid to first order in the density of scatterers. Our exact formula allows a systematic calculation of corrections to this low-density approximation. The formula is based on a renormalized cluster expansion which was presented earlier.     

Wave propagation in a disordered array of monopole scatterers

We study scalar wave propagation in a disordered static array of spherical scatterers. Due to a hard core repulsion the scatterers do not overlap. The wave is scattered by a δ-function potential at the center of each of the spheres. To this monopole model we apply the previously developed cluster expansion for the self-energy. We find the root of the dispersion equation for the coherent wave for a range of volume fraction⁵. It turns out that the monopole model develops an instability when the scattering is too strong.     

Appearance of pseudo-band-gaps in a disordered quantum wire array

The density of states and the conductivity are calculated in lateral superlattices with disorder in the period within a self-consistent Born approximation. Although the potential loses its periodicity on average due to disorder, it leads to an opening up of a pseudo-band-gap and modifies the conductivity perpendicular to the superlattice even qualitatively, when the energy reaches the zone boundary.     

Optical potential of a disordered array of scatterers

We study the propagation of scalar waves in a disordered array of static scatters. We derive a cluster expansion for the optical potential in analogy to that for the dielectric constant of a polarizable suspension. It is shown that the long range of the free space Green function leads to divergence of the cluster integrals at low energy. The divergences are removed by a resummation procedure analogous to the resummation of Mayer cluster integrals in the theory of electrolytes. We derive expressions for the most important contributions to the optical potential.     

The reference wave solution for a two-frequency wave propagating in a random medium

In this work a new reference wave method for solving parabolic-type equations is proposed. The performance of the method is demonstrated by applying it to the equation governing the propagation of the two-frequency mutual coherence function in a random medium. An analytic solution is presented for arbitrary correlation properties of the medium. It is shown that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extensions to more general types of media are considered.     

Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z ^d , 〈,〉 denotes nearest neighbors inZ ^d ;J>0 andh={h(x)>0,x∈Z ^d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h ^?δ dμ(h)<∞ for some δ>0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z ^d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _x,h,J <∞.     

Transmission and reflection of waves in a one-dimensional disordered array

We study wave propagation in a one-dimensional disordered array of scattering potentials. We calculate the mean and the variance of the resistance of the array, defined as the ratio of reflected to transmitted intensity, for a rather wide class of probability distributions characterizing the disorder. Our method is based on a mapping of the wave propagation onto the motion of a two-dimensional oscillator which is perturbed parametrically.     

Suppressing amplitude fluctuations of the wave propagating in a randomly inhomogeneous medium

We suggest using spatial processing of the wave field with the aid of the double (in source and observer coordinates) weighted Fourier transform (DWFT) to suppress amplitude fluctuations (amplitude scintillations) during wave propagation in a randomly inhomogeneous medium. We examine the influence of sizes of receiving and transmitting antenna systems on the efficiency of the spatial processing in suppressing scintillations for both weak and strong intensity fluctuations. We demonstrate that the efficiency of the suppression of amplitude fluctuations by the inverse DWFT depends on the excess of sizes of fan beam projections of receiving and transmitting antenna systems over the Fresnel radius in a region with irregularities.     

Mean field of a low-frequency sound wave propagating in a fluctuating ocean

Statistical characteristics of low-frequency sound waves propagating over long distances in a fluctuating ocean are important for many practical problems. In this paper, using the theory of multiple scattering, the mean field of a low-frequency sound wave was analytically calculated. In these calculations, the ratio of the sound wavelength and the scale of random inhomogeneities can be arbitrary. Furthermore, the correlation function of inhomogeneities is expressed in terms of a modal spectrum (e.g., internal waves modes). The obtained mean sound field is expressed as a sum of normal modes that attenuate exponentially. It is shown that the extinction coefficients of the modes are linearly related to the spectrum of random inhomogeneities in the ocean. Measurements of the extinction coefficients can therefore be used for retrieving this spectrum. The mean sound field is calculated for both 3D and 2D geometries of sound propagation. The results obtained can be used to study the range of applicability of the 2D propagation model.     

Equilibrium state of charged particles in a wave propagating along the magnetic field

This investigation examines the adiabatic motion of a charged particle near the equilibrium state in a field of a plane, circularly polarized, electromagnetic wave which is propagating with a changing velocity phase along the magnetic field. Approximate equations are found which describe the behavior of the equilibrium state parameters when the wave leaves the medium and enters a vacuum. It is shown that compared to the equilibrium value in this situation under the adiabatic approximation there is a decrease in amplitude of the particle energy fluctuation; this establishes the possibility of a prolonged acceleration of the particle to high energies. It is further demonstrated that a particle moving close to equilibrium state can appear to be in the autoresonance regime when the wave enters vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 117–122, October, 1976.     

The dynamics of a polariton dimer in a disordered coupled array of cavities

We investigate the effect of disorder in the laser intensity on the dynamics of dark-state polaritons in an array of 20 cavities, each containing an ensemble of four-level atoms that is described by a Bose-Hubbard Hamiltonian. We examine the evolution of the polariton number in the cavities starting from a state with either one or two polaritons in one of the cavities. For the case of a single polariton without disorder in the laser intensity, we calculate the wavefunction of the polariton and find that it disperses away from the initial cavity with time. The addition of disorder results in minimal suppression of the dispersal of the wavefunction. In the case of two polaritons with an on-site repulsion to hopping strength ratio of 20, we find that the polaritons form a repulsively bound state or dimer. Without disorder the dimer wavefunction disperses similarly to the single polariton wavefunction but over a longer time period. The addition of sufficiently strong disorder results in localization of the polariton dimer. The localization length is found to be described by a power law with exponent ? 1.31. We also find that we can localise the dimer at any given time by switching on the disorder.     

Giant fluctuations of topological charge in a disordered wave guide

We study the fluctuations of the total topological charge of a scalar wave propagating in a hollow conducting waveguide filled with scatterers inside. We investigate the dependence of the screening on the scattering mean free path and on the presence of boundaries. Near the cut-off frequencies of the waveguide, screening is strongly suppressed close to boundaries. The resulting huge fluctuations of the total topological charge are very sensitive to the disorder.     

Phase velocity of a transverse electric wave propagating in a magnetized electron beam

In this paper three-dimentional simulations are carried out to the phase velocity of a transverse electric wave which propagates in a relativistic electron beam magnetized by a wiggler field and an axial guide magnetic field. Results show that the phase velocities are quite different from each other as the axial guide magnetic field changes its direction.     

On the two-scale expansion of the fourth moment of a wave propagating in a random medium

Abstract

A comprehensive and rigorous analysis of the prevalent version of the two-scale expansion used to solve the fourth-moment equation shows that it is not an asymptotic technique. The correct asymptotic version is derived and found to be analytically non-tractable. An elaborated interpretation to the correction terms used before is established and shows that an additional term of the same order was overlooked. The new expression which will improve the result in the scintillation peak is offered. The role of the small parameter of the problem is discussed.