Quantum Unique Ergodicity for Cayley graphs of quasirandom groups

Magee, Michael; Thomas, Joe; Zhao, Yufei

Abstract

A finite group G is called C-quasirandom (by Gowers) if all non-trivial irreducible complex representations of G have dimension at least C. For any unit ℓ2 function on a finite group we associate the quantum probability measure on the group given by the absolute value squared of the function. We show that if a group is highly quasirandom, in the above sense, then any Cayley graph of this group has an orthonormal eigenbasis of the adjacency operator such that the quantum probability measures of the eigenfunctions put close to the correct proportion of their mass on suitably selected subsets of the group that are not too small.

Citation

Magee, M., Thomas, J., & Zhao, Y. (2023). Quantum Unique Ergodicity for Cayley graphs of quasirandom groups. Communications in Mathematical Physics, 402, 3021-3044. https://doi.org/10.1007/s00220-023-04801-x

• Journal Article Type: Article
• Acceptance Date: Jun 15, 2023
• Online Publication Date: Jul 31, 2023
• Publication Date: Jul 31, 2023
• Deposit Date: Jul 19, 2023
• Publicly Available Date: Aug 1, 2024
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 402
• Pages: 3021-3044
• DOI: https://doi.org/10.1007/s00220-023-04801-x
• Public URL: https://durham-repository.worktribe.com/output/1168252
• Publisher URL: https://doi.org/10.1007/s00220-023-04801-x