Communications in Mathematical Physics

, Volume 238, Issue 3, pp 505–524 | Cite as

Regular Spacings of Complex Eigenvalues in the One-Dimensional Non-Hermitian Anderson Model

  • Ilya Ya. Goldsheid
  • Boris A. Khoruzhenko


We prove that in dimension one the non-real eigenvalues of the non-Hermitian Anderson (NHA) model with a selfaveraging potential are regularly spaced. The class of selfaveraging potentials which we introduce in this paper is very wide and in particular includes stationary potentials (with probability one) as well as all quasi-periodic potentials. It should be emphasized that our approach here is much simpler than the one we used before. It allows us a) to investigate the above mentioned spacings, b) to establish certain properties of the integrated density of states of the Hermitian Anderson models with selfaveraging potentials, and c) to obtain (as a by-product) much simpler proofs of our previous results concerned with non-real eigenvalues of the NHA model.


Simple Proof Stationary Potential Anderson Model Complex Eigenvalue Regular Spacing 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ilya Ya. Goldsheid
    • 1
  • Boris A. Khoruzhenko
    • 1
  1. 1.School of Mathematical Sciences, Queen MaryUniversity of LondonLondonU.K

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