Distribution of Eigenvalues in Non-Hermitian Anderson Model

Details Distribution of Eigenvalues in Non-Hermitian Anderson Model Distribution of Eigenvalues in Non-Hermitian Anderson Model

1997-07-22

arxiv.org/abs/cond-mat/9707230v1

Phys. Rev. Lett. Vol.80 (1998) 2897-2900

Physics

Condensed Matter

6 pages (LaTeX)

Scientific paper

10.1103/PhysRevLett.80.2897

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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