School of Mathematical Sciences
Monday, Decmeber 5, 2011
Schreiber 006, 12:15
Technical University in Munich and Princeton University
Resonances and absolutely continuous spectra of random operators on tree graphs
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 a tree graph. Among the surprising phenomena which we discover is that even at weak disorder the regime of absolutely continuous states extends well beyond the one of the graph Laplacian. As will be explained in the lecture, the mathematical mechanism for the appearance of absolutely continuous states in this non-perturbative regime are disorder-induced resonances.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006