Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System

Details Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System

2007-06-21

arxiv.org/abs/0706.3129v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 1 figure

Scientific paper

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.

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