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

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

Automated summary

This study develops the kinetic theory of classical and quantum particles in gravitational interaction, with a focus on the applications of quantum particle kinetic theory in the context of dark matter. The main properties of the quantum Landau equation and its implications for bosonic particles, especially in Bose-Einstein condensation, are discussed. The study also examines the relationship with the works of other researchers in the field of dark matter and Bose stars formation.