Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder

Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder

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Simone Warzel, TU- Munich
Jadwin Hall A06

We discuss recently established criteria for the formation of extended states on tree graphs in the presence of disorder. These criteria have the surprising implication that for bounded random potentials, as in the Anderson model, in the weak disorder regime there is no transition to a spectral regime of Anderson localization in the form usually envisioned.