Eigenvalue distributions of large Euclidean random matrices for waves in random media

Euclidean random matrices and their applications in physics

We review the state of the art of the theory of Euclidean random matrices, focusing on the density of their eigenvalues. Both Hermitian and non-Hermitian matrices are considered and links with simpler, standard random matrix ensembles are established. We discuss applications of Euclidean random matrices to contemporary problems in condensed matter physics, optics, and quantum chaos.

Transmission eigenvalues in random media with surface reflection

The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically that the distribution of transmission eigenvalues of diffusive waves exhibits a nonanalytic `transition' as the strength of surface reflection at one surface passes through a critical value while that at the other is fixed. Above the critical value, the highest transmission eigenvalue is strictly smaller than unity and decreases with increasing internal ref…

基于辐射场理论的 disordered media 透射本征值分布

Transmission eigenvalue distribution in disordered media from radiant field theory

本文提出辐射场理论，通过自洽矩阵辐射度输运方程计算无序介质透射本征值分布，突破随机矩阵模型宏观假设，覆盖准弹道与扩散区域并适用于开放几何结构。

Non-Hermitian Euclidean random matrix theory

We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave propagation in an ensemble of point-like scattering centers. This opens a new perspective in the study of wave diffusion, Anderson localization, and random lasing.

Survival probability and order statistics of diffusion on disordered media

We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem we assume that, for short times, the survival probability (the probability that a single random walker is not absorbed by a hyperspherical surface during some time interval) decays for disordered media in the same way as for Euclidean and some class of deterministic fractal lattices. This conjecture is checked by simulation on the incipient percolation aggr…

Shape-dependence of transmission, reflection and absorption eigenvalue densities in disordered waveguides with dissipation

The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems un- derpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced transmission in optics and acoustics. Here, we show that in the presence of absorption, density of the transmission eigenvalues depends on the confinement geometry of scattering media. Furthermore, in an asymmetric waveguide, densities of the reflection and absorption eigenvalues also depend of the side from which the waves are incident. With increas- ing absorpotion,…