Göttingen 2012 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 4: HV Quantenmechanik: S. Warzel

MP 4.1: Invited Talk

Tuesday, February 28, 2012, 14:15–14:55, ZHG 003

Delocalization through resonances: the Anderson transition on trees — •Simone Warzel — Fine Hall, Princeton University — Zentrum Mathematik, TUM

Motivated by the quest for a theory of quantum transport in disordered media, in 1958 P.W. Anderson came up with a model for a quantum particle in a random energy landscape. Among its interesting features is a conjectured sharp transition from a regime of localized eigenstates to one of diffusive transport. Until today it remains a mathematical challenge to establish these features in the framework of random Schrödinger operators.

In this talk, I will describe recent progress in the understanding of the spectral and dynamical properties of such operators in case the underlying configuration space is hyperbolic such as a tree graph. Among the surprising phenomena which we discover is that even at weak disorder the regime of diffusive transport extends well beyond the one of the graph Laplacian into the regime of Lifshitz tails. As will be explained in the lecture, the mathematical mechanism for the appearance of conducting states in this non-perturbative regime are disorder-induced resonances.