Localization and mobility edge for sparsely random potentials

Details Localization and mobility edge for sparsely random potentials Localization and mobility edge for sparsely random potentials

1998-05-18

arxiv.org/abs/math-ph/9805015v2

Physics

Mathematical Physics

Completely revised, main theorems modified; latex2e file

Scientific paper

In this paper we consider sparsely random potentials in 5 or more dimensional
cubic lattice and exhibit localized and extended states. We identify also the
mobility edge for a class of potentials going to infinity at infinity. Our
treatment includes a large class of unperturbed selfadjoint opeartors commuting
with the usual Laplacian on the lattice.

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