Analysis seminar: Søren Mikkelsen

Speaker: Søren Mikkelsen, University of Bath.

Title: Schrödinger evolution in a low-density random potential: convergence to solutions of the linear Boltzmann equation

Abstract: It is a fundamental problem in mathematical physics to derive macroscopic transport equations from the underlying microscopic transport equations. In this talk, we will consider such a problem. To be precise we will consider solutions to a time-dependent Schrödinger equation for a potential localised at the points of a Poisson point process. For these solutions we will present a result stating that the phase-space distribution converges in the annealed Boltzmann-Grad limit to a semiclassical Wigner measure which solves the linear Boltzmann equation.