TY - JOUR
T1 - Quantum ergodicity for the Anderson model on regular graphs
AU - Anantharaman, Nalini
AU - Sabri, Mostafa
N1 - Funding Information:
This material is based uponwork supported by the Agence Nationale de la Recherche under Grant No. ANR-13-BS01-0007-01, by the Labex IRMIA and the Institute of Advance Study of Université de Strasbourg, and by Institut Universitaire de France.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - 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.
AB - 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.
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U2 - 10.1063/1.5000962
DO - 10.1063/1.5000962
M3 - Article
AN - SCOPUS:85030473396
SN - 0022-2488
VL - 58
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 9
M1 - 091901
ER -