Title

Discrete Bethe–Sommerfeld Conjecture

Document Type

Article

Publication Date

7-1-2018

Abstract

In this paper, we prove a discrete version of the Bethe–Sommerfeld conjecture. Namely, we show that the spectra of multi-dimensional discrete periodic Schrödinger operators on Zd lattice with sufficiently small potentials contain at most two intervals. Moreover, the spectrum is a single interval, provided at least one of the periods is odd, and can have a gap whenever all periods are even.

Publication Source (Journal or Book title)

Communications in Mathematical Physics

First Page

205

Last Page

216

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