title: Anderson localization on the Bethe lattice: nonergodicity of extended States.
abstract: Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions f(α) defined in Eq. (3) remains positive for α noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization; i.e., the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.
authors.affiliation: Laboratoire de Physique Théorique de l'ENS and Institut de Physique Theorique Philippe Meyer 24, Rue Lhomond, 75005 Paris, France.
authors.forename: A
authors.initials: A
authors.lastname: De Luca
authors.affiliation: Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA.
authors.forename: B L
authors.initials: BL
authors.lastname: Altshuler
authors.affiliation: Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy and L. D. Landau Institute for Theoretical Physics, 2 Kosygina Street, 119334 Moscow, Russia.
authors.forename: V E
authors.initials: VE
authors.lastname: Kravtsov
authors.affiliation: Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA and Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy and Physics Department, Princeton University, Princeton, New Jersey 08544, USA and INFN, Sezione di Trieste, Strada Costiera 11, 34151 Trieste, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Scardicchio