Effectively describing the long-time dynamical behavior of quantum systems is a long-standing open problem. When the coupling constant $\lambda$ of the interaction is small, the dynamics of the system up to kinetic time $t \sim \lambda^{-2}$ is conjectured to be effectively governed by the Boltzmann-Nordheim kinetic equation. In this talk, we consider a system of weakly interacting lattice fermions at thermal equilibrium, and I will describe how the two-point time correlation function of the system depends on the equilibrium solution of the Boltzmann-Nordheim equation. We approach the problem using a perturbation expansion and represent the appearing terms by Feynman diagrams.

This is joint work with Phan Thành Nam, Herbert Spohn, and Minh-Binh Tran.