Fractional random Schrödinger operators, integrated density of states and localisation

Fractional random Schrödinger operators, integrated density of states and localisation

In this talk we will review some recent results on the fractional Anderson model, a random Schrödinger operator driven by a fractional laplacian. The interest on the latter lies in their association to stable Levy processes, random walks with long jumps and anomalous diffusion.

We discuss in this talk the interplay between the non-locality of the fractional laplacian and the localisation 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 is based on joint work with M. Gebert (LMU Munich).

Speaker

Constanza Rojas-Molina, CY Tech - Institut des Sciences et Techniques - CY Cergy Paris Université

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia (jesus.martinez-garcia@essex.ac.uk)