Scaling theory of the Anderson transition in random graphs: ergodicity and universalityReport as inadecuate




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1 Instituto de Investigaciones Físicas de Mar del Plata 2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques 3 Information et Chaos Quantiques LPT LPT - Laboratoire de Physique Théorique - IRSAMC 4 Institut de Physique Nucl-eaire, Atomique et de Spectroscopie

Abstract : We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1 < K ≤ 2, through a combination of large scale numerical simulations and finite-size scaling analysis. We find that a single Anderson transition separates a localized phase from an unusual delocalized phase which is ergodic at large scales but strongly non-ergodic at smaller scales. The critical regime is characterized by multifractal wavefunctions located on few branches of the graph. Two different scaling laws apply on both sides of the transition: a linear scaling as a function of the linear size of the system on the localized side, and an unusual volumic scaling on the delocalized side. The critical scalings and exponents are found to be independent of the branching parameter and should describe all infinite dimensional random graphs without boundary.

Keywords : transition random graphs ergodicity Anderson localization





Author: Ignacio Garcia-Mata - Olivier Giraud - Bertrand Georgeot - John Martin - Rémy Dubertrand - Gabriel Lemarié -

Source: https://hal.archives-ouvertes.fr/



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