We study the dynamics of a test particle in a system of $N$ randomly distributed stationary spherical obstacles (scatterers) in dimensions $d \geq 2$. We assume that the test particle's motion is influenced by two contributing factors. One contribution comes from collisions with scatterers, whose interaction potential is modelled by $\varepsilon^\alpha U(r/\varepsilon)$, where $\alpha \in (0,1/2]$ and $U$ is radially symmetric and strictly decreasing. The second factor is a long range force field of mean-field type generated by the collection of all scatterers in the system. In the weak coupling regime, we prove that for $\alpha \in (0,(d-1)/8)$ the test particle's probability density converges to the solution of the linear Landau-Vlasov equation as $\varepsilon \to 0$.
This talk is based on joint work with Chiara Saffirio.