Relaxation in a Fuzzy Dark Matter Halo. II. Self-consistent kinetic
  equations
  Fuzzy dark matter (FDM) is composed of ultra-light bosons having a de Broglie
wavelength that is comparable to the size of the stellar component of galaxies
at typical galactic velocities. FDM behaves like cold dark matter on large
scales. However, on the scale of the de Broglie wavelength, an FDM halo
exhibits density fluctuations that lead to relaxation, a process similar to the
two-body relaxation that occurs in classical gravitational N-body systems and
is described by the Fokker-Planck equation. We derive the FDM analog of that
kinetic equation, and solve it to find the evolution of the velocity
distribution in a spatially homogeneous FDM halo. We also determine the
dielectric function and the dispersion relation for linear waves in an FDM
halo.
