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arXiv · 1707.03482

Discrete Bethe-Sommerfeld Conjecture

Rui Han·Svetlana Jitomirskaya
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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 $\mathbb{Z}^d$ lattice with sufficiently small potentials contain at most two intervals. Moreover, the spectrum is a single interval, provided one of the periods is odd, and can have a gap whenever all periods are even.

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Rui Han, Svetlana Jitomirskaya. 2017-07-11. Discrete Bethe-Sommerfeld Conjecture. https://doi.org/10.1007/s00220-018-3141-9

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