Large-scale limits of interacting particle systems

IHÉS, France / October 4-8, 2021

**Jens Marklof** (University of Bristol)

*Quantum Lorentz gas in the Boltzmann-Grad limit: random vs periodic.*

A major challenge in the kinetic theory of gases is to establish the convergence of the dynamics to a macroscopic transport process described by the appropriate kinetic equation. In the case of the quantum Lorentz gas with random potentials, important studies of Spohn, Erdos-Yau, Eng-Erdos and others have identified the linear Boltzmann equation as the correct limit. In this lecture I will discuss periodic potentials in the Boltzmann-Grad scaling, and report on a new limiting random process which is incompatible with the linear Boltzmann equation. Based on joint work with Jory Griffin (Oklahoma), *J. Stat. Phys.* **184** (2021).