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

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.

5 pages, 1 figure

References in corpus (5)

• Random Matrices close to Hermitian or unitary: overview of methods and results
• Information capacity of optical fiber channels with zero average dispersion
• Large scale correlations in normal and general non-Hermitian matrix ensembles
• Infinite Products of Large Random Matrices and Matrix-valued Diffusion
• Schrodinger equation with a spatially and temporally random potential: Effects of cross-phase modulation in optical communication

Cited by in corpus (3)

• Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation
• Nonlinear propagation of an optical speckle field
• Some results on discrete eigenvalues for the Stochastic Nonlinear Schroedinger Equation in fiber optics