Landau equation for self-gravitating classical and quantum particles: Application to dark matter

We develop the kinetic theory of classical and quantum particles (fermions bosons) in gravitational interaction. The kinetic theory of quantum may have applications in the context of dark matter. For simplicity, consider an infinite and spatially homogeneous system (or make a local) and neglect collective effects. This leads to the quantum Landau derived heuristically in Chavanis, Physica A 332, 89 (2004). We its main properties: conservation laws, H-theorem, equilibrium, relaxation time, quantum diffusion and friction coefficients, quantum potentials, self-consistent evolution, (thermal) bath approximation, Fokker-Planck equation, quantum King model. . . For bosonic particles, Landau equation can describe the process of Bose-Einstein condensation. We the relation of our study with the works of Levkov et al. , Phys. Rev. . 121, 151301 (2018) ; Bar-Or et al. , Astrophys. J. 871, 28 (2019) on fuzzy matter halos and the formation of Bose stars and solitons.