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

Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri, Brian Winn

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)28-98
Number of pages71
JournalJournal des Mathematiques Pures et Appliquees
Volume151
DOIs
StatePublished - Jul 2021

Keywords

  • Delocalization
  • Quantum ergodicity
  • Quantum graphs
  • Trees

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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