Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System
Disordered Systems and Neural Networks
2013-05-29 v2 Statistical Mechanics
Information Theory
math.IT
Exactly Solvable and Integrable Systems
Abstract
We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive non-linear Schroedinger equation with a Gaussian random pulse as initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of the information transmission through non-linear optical fibers.
Keywords
Cite
@article{arxiv.0706.3129,
title = {Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System},
author = {Pavlos Kazakopoulos and Aris L. Moustakas},
journal= {arXiv preprint arXiv:0706.3129},
year = {2013}
}
Comments
5 pages, 1 figure