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

TL;DR

This paper develops a kinetic theory framework for classical and quantum particles under gravity, deriving a quantum Landau equation with applications to dark matter, Bose-Einstein condensation, and astrophysical phenomena.

Contribution

It introduces a quantum Landau equation for self-gravitating particles, detailing its properties and potential applications in dark matter and Bose-Einstein condensation.

Findings

Derived the quantum Landau equation and its properties.

Established the connection with Bose-Einstein condensation.

Discussed applications to dark matter halos and Bose stars.

Abstract

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 [Chavanis, 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); Bar-Or et al., Astrophys. J. 871, 28 (2019)] on fuzzy dark matter halos and the formation of Bose stars and solitons.