TY - JOUR

T1 - Quantum Ergodicity for Periodic Graphs

AU - McKenzie, Theo

AU - Sabri, Mostafa

N1 - Funding Information:
T. McKenzie: Supported by NSF GRFP Grant DGE-1752814 and NSF Grant DMS-2212881.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023/11

Y1 - 2023/11

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-023-04826-2

DO - 10.1007/s00220-023-04826-2

M3 - Article

AN - SCOPUS:85171556305

SN - 0010-3616

VL - 403

SP - 1477

EP - 1509

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -