Scaling limits in Kinetic theory
Summer School - Lyon - 2019

Minicourse by Herbert Spohn (TU München)

Kinetic limit for weakly nonlinear wave equations

In condensed matter physics, linear and nonlinear kinetic equations are a standard tool. Formally they are derived from a system of interacting quantum particles. Closely related are classical nonlinear wave equations, which allow for a somewhat simpler mathematical framework. In physics they are studied in the theory of wave turbulence. In my course, I will give an introduction to the kinetic limit for waves. In the second half, I will focus on the nonlinear Schrödinger equation on a lattice with a weak on-site nonlinearity. The latter part is based on joint work with J. Lukkarinen.