Discrete Bethe-Sommerfeld conjecture

DOI10.1007/S00220-018-3141-9zbMath1403.35190arXiv1707.03482OpenAlexW3102780931WikidataQ123116807 ScholiaQ123116807MaRDI QIDQ1663626

Rui Han, Svetlana Ya. Jitomirskaya

Publication date: 21 August 2018

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.03482

zbMATH Keywords

spectrumBethe-Sommerfeld conjecture(discrete) Schrödinger operator on the multi-dimensional integer lattice

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Pseudodifferential operators (47G30)

Related Items (12)

Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues ⋮ Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications ⋮ Topics on Fermi varieties of discrete periodic Schrödinger operators ⋮ On spectral bands of discrete periodic operators ⋮ Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set ⋮ Discrete Bethe-Sommerfeld conjecture for triangular, square, and hexagonal lattices ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ Multidimensional almost-periodic Schrödinger operators with Cantor spectrum ⋮ On the spectra of separable 2D almost Mathieu operators ⋮ On direct integral expansion for periodic block-operator Jacobi matrices and applications ⋮ Spectra of discrete two-dimensional periodic Schrödinger operators with small potentials ⋮ The landscape law for tight binding Hamiltonians

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• Perturbation theory for the Schrödinger operator with a periodic potential
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