Quantum ergodicity for the Anderson model on regular graphs

Abstract : 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, and that the dynamical transport is ballistic. In this work, we prove that in such 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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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01503952
Contributeur : Mostafa Sabri <>
Soumis le : samedi 7 octobre 2017 - 11:04:06
Dernière modification le : jeudi 12 octobre 2017 - 01:03:43

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Nalini Anantharaman, Mostafa Sabri. Quantum ergodicity for the Anderson model on regular graphs. 2017. 〈hal-01503952v2〉

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