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arXiv · 2208.12685

Quantum ergodicity for periodic graphs

Theo Mckenzie·Mostafa Sabri
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Abstract

We prove quantum ergodicity for a family of periodic Schr\"odinger operators $H$ on periodic graphs. This means that most eigenfunctions of $H$ on large finite periodic graphs are equidistributed in some sense, hence delocalized. Our results cover the adjacency matrix on $\mathbb{Z}^d$, the triangular lattice, the honeycomb lattice, Cartesian products and periodic Schr\"odinger operators on $\mathbb{Z}^d$. The theorem applies more generally to any periodic Schr\"odinger operator satisfying an assumption on the Floquet eigenvalues.

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Theo Mckenzie, Mostafa Sabri. 2022-08-26. Quantum ergodicity for periodic graphs. https://arxiv.org/abs/2208.12685

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