Non-Hermitian Euclidean random matrix theory

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

We study probability distributions of eigenvalues of Hermitian and non-Hermitian Euclidean random matrices that are typically encountered in the problems of wave propagation 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.

Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles

Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre's ensemble, in which each matrix element is an independent, identically distributed Gaussian complex random variable. The other is a simpler calculation using $N^{-1}$ as an expansion parameter, where $N$ is the rank of the random matrix: this is applied to Girko's ensemble. Consequences of eigenvector correlations which may be of physical importance in applicati…

曲率诱导的非厄米安德森转变中的几何普适性

Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions

本研究通过双曲晶格上的非厄米安德森转变，发现空间曲率可定义新的普适类，其临界指数接近平均场值，表明曲率是超越维度与对称性的普适性组织原则。

Eigenvector statistics in non-Hermitian random matrix ensembles

We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary parts of each element of an N x N matrix, J, are independent random variables. Calculating ensemble averages based on the quantity $< L_α| L_β> < R_β| R_α>$, where $< L_α|$ and $| R_β>$ are left and right eigenvectors of J, we show for large N that eigenvectors associated with a pair of eigenvalues are highly correlated if the two eigenvalues lie close in the complex plane. We examine consequences of these correlations that …

非厄米 Rosenzweig-Porter 随机矩阵系综：对分形相的阻碍

Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase

本文将 Rosenzweig-Porter 随机矩阵系综推广到非厄米情形，发现遍历相和局域相保持稳定，而分形相仅在纯实或纯虚对角势下存在，在一般复对角势下消失并转为局域相。