Regular spacings of complex eigenvalues in the one-dimensional non-Hermitian Anderson Model
I.Ya. Goldsheid and B.A. Khoruzhenko
Abstract.
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.
Ilya Goldsheid and Boris Khoruzhenko
School of Mathematical Sciences
Queen Mary, University of London
London E1 4NS, UK
i.goldsheid@qmul.a.c.uk
b.khoruzhenko@qmul.a.c.uk