Quantum Ergodicity for Periodic Graphs

Theo McKenzie, Mostafa Sabri

Research output: Contribution to journalArticlepeer-review


This article shows that for a large class of discrete periodic Schrödinger operators, most wavefunctions resemble Bloch states. More precisely, 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 Zd , the triangular lattice, the honeycomb lattice, Cartesian products, and periodic Schrödinger operators on Zd . The theorem applies more generally to any periodic Schrödinger operator satisfying an assumption on the Floquet eigenvalues.

Original languageEnglish (US)
Pages (from-to)1477-1509
Number of pages33
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Nov 2023

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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