Non-Hermitian Euclidean random matrix theory
Abstract
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 pointlike scattering centers. This opens a new perspective in the study of wave diffusion, Anderson localization, and random lasing.
- Publication:
-
Physical Review E
- Pub Date:
- July 2011
- DOI:
- 10.1103/PhysRevE.84.011150
- arXiv:
- arXiv:1102.1850
- Bibcode:
- 2011PhRvE..84a1150G
- Keywords:
-
- 05.40.-a;
- 05.45.Mt;
- 02.10.Yn;
- 42.25.Dd;
- Fluctuation phenomena random processes noise and Brownian motion;
- Quantum chaos;
- semiclassical methods;
- Matrix theory;
- Wave propagation in random media;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 11 pages, 9 figures