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Quantum ergodicity for expanding quantum graphs in the regime of spectral delocalization

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posted on 2021-03-04, 14:15 authored by Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri, Brian WinnBrian Winn
We consider a sequence of finite quantum graphs with few loops, so that they converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree. We assume these quantum trees are spectrally delocalized in some interval I, in the sense that their spectrum in I is purely absolutely continuous and their Green’s functions are well controlled near the real axis. We furthermore suppose that the underlying sequence of discrete graphs is expanding. We deduce a quantum ergodicity result, showing that the eigenfunctions with eigenvalues lying in I are spatially delocalized.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal de Mathematiques Pures et Appliquees

Volume

151

Pages

28-98

Publisher

Elsevier

Version

  • AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Journal de Mathematiques Pures et Appliquees and the definitive published version is available at https://doi.org/10.1016/j.matpur.2021.04.012.

Acceptance date

2021-02-23

Publication date

2021-04-06

Copyright date

2021

ISSN

0021-7824

Language

  • en

Depositor

Dr Brian Winn . Deposit date: 3 March 2021

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