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Distribution of Eigenvalues in Non-Hermitian Anderson Model

Ilya Ya. Goldsheid·Boris A. Khoruzhenko
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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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Ilya Ya. Goldsheid, Boris A. Khoruzhenko. 1997-07-22. Distribution of Eigenvalues in Non-Hermitian Anderson Model. https://doi.org/10.1103/physrevlett.80.2897

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