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arXiv · 2210.10532

Bloch varieties and quantum ergodicity for periodic graph operators

Wencai Liu
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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 Schr\"odinger operators on $\mathbb{Z}^d$ 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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Wencai Liu. 2022-10-19. Bloch varieties and quantum ergodicity for periodic graph operators. https://arxiv.org/abs/2210.10532

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