Distribution of Eigenvalues in Non-Hermitian Anderson Model

Preprint

22 July 1997

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/9707230

Abstract

We develop a theory which describes the behaviour of eigenvalues of a class of one-dimensional random non-Hermitian operators introduced recently by Hatano and Nelson. Under general assumptions on random parameters we prove that the eigenvalues are distributed along a curve in the complex plane. An equation for the curve is derived and the density of complex eigenvalues is found in terms of spectral characteristics of a ``reference'' hermitian disordered system. Coexistence of the real and complex parts in the spectrum and other generic properties of the eigenvalue distribution for the non-Hermitian problem are discussed.

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All Related Versions

Version 1, 1997-07-22, ArXiv
Version 1, 2017-07-07, ArXiv (Unconfirmed version)
Published version: Physical Review Letters, 80 (13), 2897.

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