Fractional random Schrödinger operators, integrated density of states and localization

Abstract: We will review some recent results on the fractional Anderson model, a random Schrödinger operator driven by a fractional laplacian. The interest of the latter lies in its association to stable Levy processes, random walks with long jumps and anomalous diffusion. We discuss the interplay between the non-locality of the fractional laplacian and the localization properties of the random potential in the fractional Anderson model, in both the continuous and discrete settings. In the discrete setting we study the integrated density of states and show a fractional version of Lifshitz tails. This coincides with results obtained in the continuous setting by the probability community. This talk is based on joint work with M. Gebert (LMU Munich).

mathematical physics

Audience: researchers in the discipline

( video )

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