Quantum ergodicity for the Anderson model on regular graphs

Nalini Anantharaman, Mostafa Sabri

Research output: Contribution to journalArticlepeer-review


We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous (AC) and that the dynamical transport is ballistic. In this work, we prove that in such an AC regime, the eigenfunctions are also delocalized in space, in the sense that if we consider a sequence of regular graphs converging to the regular tree, then the eigenfunctions become asymptotically uniformly distributed. The precise result is a quantum ergodicity theorem.

Original languageEnglish (US)
Article number091901
JournalJournal of Mathematical Physics
Issue number9
StatePublished - Sep 1 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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