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

Understand

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)].