Non-Hermitian Euclidean random matrix theory

A. Goetschy (1) , S. E. Skipetrov (1)

1 LPM2C - Laboratoire de physique et modélisation des milieux condensés

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]

A. Goetschy, S. E. Skipetrov. Non-Hermitian Euclidean random matrix theory. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 84 (1), pp.011150. ⟨10.1103/PhysRevE.84.011150⟩. ⟨hal-00565312⟩