Dresden 2017 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 11: Critical phenomena
DY 11.8: Vortrag
Montag, 20. März 2017, 17:30–17:45, HÜL 186
Scaling theory of the Anderson transition in random graphs: ergodicity and universality — •Remy Dubertrand1, Ignacio Garcia-Mata2, Olivier Giraud3, Bertrand Georgeot4, John Martin1, and Gabriel Lemarie4 — 1IPNAS CESAM Université de Liège, Liège, Belgium — 2IFIMAR CONICET-UNMdP, Mar del Plata, Argentina — 3LPTMS CNRS Université Paris-Sud, Orsay, France — 4LPT IRSAMC Université de Toulouse CNRS, Toulouse, France
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1< K≤ 2, through large scale numerical simulations and finite-size scaling analysis. This problem has attracted a renewed attractivity and is currently hotly debated [1,2,3].
We find that a single 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 scalings and exponents are independent of the branching parameter, which strongly supports the universality of our results. During the talk I will describe the results presented in [4] and stress the unusual features of the Anderson transition we find on these random graphs.
[1] B. Altshuler et al., arXiv:1605.02295 (2016)
[2] K. Tikhonov et al., arXiv:1604.05353 (2016)
[3] D. Facoetti et al., arXiv:1607.05942 (2016)
[4] I. Garcia-Mata et al., arXiv:1609.05857 (2016)