Backscattering enhancement phenomenon in a random medium is studied by numerically analyzing a bistatic radar cross-section of a circular cylinder, under the condition that the spatial coherence length of the incident waves around the cylinder is larger enough than the size of the cylinder. The numerical analysis shows that the phenomenon may occur not only in the backward direction but also in...

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order √ ε. The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit ε → 0 the disorder averaged Wigner function on the kinetic scale, time and space of order ε, is governed...

We consider the basis for describing strong scattering in terms of diffusive processes based on the diffusion equation. Intermediate strength scattering is then considered in terms of a fractional diffusion equation which is studied using results from fractional calculus. This approach is justified in terms of the generalization of a random walk model with no statistical bias in the phase to a ...

2014 The effect of a random potential on the diffusion coefficient of a polymer is shown to be a relevant perturbation in the renormalization group sense below four dimensions. Attempts to « improve » the perturbation expansion by means of the renormalization group failed as it was not possible to locate a stable accessible fixed point. Speculations on the physical implications of these results...

We study the competing effects of stimulated and spontaneous emission on the information capacity of an amplifying disordered waveguide. At the laser threshold the capacity reaches a "universal" limit, independent of the degree of disorder. Whether or not this limit is larger or smaller than the capacity without amplification depends on the disorder, as well as on the input power. Explicit expr...

Light-wave propagation in a randomly scattering but uniformly and coherently amplifying optical medium is analysed for the statistics of the coefficient of reflection r(l) that may now exceed unity, hence super-reflection. Uniform coherent amplification is introduced phenomenologically through a constant negative imaginary part added to the otherwise real dielectric constant of the medium, assu...

Abstract We are concerned with scaling limits of the solutions to stochastic differential equations with stationary coefficients driven by Poisson random measures and Brownian motions. We state an annealed convergence theorem, in which the limit exhibits a diffusive or superdiffusive behavior, depending on the integrability properties of the Poisson random measure.

We present a mathematical approach that simplifies the theoretical treatment of electromagnetic localization in random media and leads to closed-form analytical solutions. Starting with the assumption that the dielectric permittivity of the medium has delta-correlated spatial fluctuations, and using Ito's lemma, we derive a linear stochastic differential equation for a one-dimensional random me...