The weak-coupling limit of large classical and quantum systems

Abstract

In this contribution we illustrate the delicate transition from the microscopic description of a particle system, given in terms of fundamental equations as the Newton or the Schrödinger equation, to the reduced kinetic picture, given in terms of the Boltzmann and Landau equations which are obtained under suitable scaling limits. Special emphasis is given to the so called weak-coupling limit. The content of the lecture is mostly devoted to the very many open problems, rather than to the few known results.