Special Seminar
Approximate spectral theory in heterogeneous media, asymptotic ballistic transport, and beyond?
In this talk I’ll consider the Schrödinger in heterogeneous media and shall discuss long-time transport properties of localized initial conditions, and more precisely the regime of asymptotic ballistic transport. To this aim I’ll introduce an approximate spectral theory inspired by the Floquet theory for periodic media that allows to diagonalize the Schrödinger operator up to an error that we control by energy estimates combined with estimates on "correctors". This yields asymptotic ballistic results for quasiperiodic potentials up to stretched exponential times, as well as fine results in the random setting. To conclude I'll discuss what direction could be taken to tackle larger time scales.
This is joint work with Mitia Duerinckx and Christopher Shirley (Université Libre de Bruxelles).