Quantum ergodicity for periodic graphs

2022/08/26 by Theo McKenzie, Mckenzie, Theo, Mostafa Sabri +1
Computer Science · Mathematics · Physics and Astronomy · #39A12 #58J51 #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2208.12685

openalex publication_date 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove quantum ergodicity for a family of periodic Schrödinger 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 ℤ^d, the triangular lattice, the honeycomb lattice, Cartesian products and periodic Schrödinger operators on ℤ^d. The theorem applies more generally to any periodic Schrödinger operator satisfying an assumption on the Floquet eigenvalues.

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