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

Mathphys Analysis Seminar

It is a fundamental problem in mathematical physics to derive macroscopic transport equation from the underlying microscopic transport equations. In this talk, we will consider problems of this kind. 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.