In the 80’s, A. Caldeira and A. Leggett initiated a research program where dissipation mechanisms are interpreted from the momentum and energy exchanges between a particle and its environment, described as a vibrational field. A few years ago, S. De Bièvre proposed a Hamiltonian model for such a situation: theoretical and numerical results show that the interactions act as a sort of friction on the particle.

The dynamic becomes more intricate when many particles are considered. We revisit this approach in the framework of statistical physics and kinetic equations. This viewpoint reveals unexpected connections with the attractive Vlasov-Poisson  system. We analyse the equilibrium states and their stability, interpreted as a Landau damping phenomenom.

The talk will present a series of results, in collaboration with A. Vavasseur (Nice), L. Vivion (Nice), R. Alonso (Rio de Janiero) et S. De Bièvre (Lille).