Bloch varieties and quantum ergodicity for periodic graph operators

2022/10/19 by Wencai Liu, Liu, Wencai · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2210.10532

openalex publication_date 2022/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For periodic graph operators, we establish criteria to determine the overlaps of spectral band functions based on Bloch varieties. One criterion states that for a large family of periodic graph operators, the irreducibility of Bloch varieties implies no non-trivial periods for spectral band functions. This particularly shows that spectral band functions of discrete periodic Schrödinger operators on ℤ^d have no non-trivial periods, answering a question asked by Mckenzie and Sabri [Quantum ergodicity for periodic graphs. arXiv preprint arXiv:2208.12685 (2022)].

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• Absence of flat bands for discrete periodic graph operators with generic potentials

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