  Dark matter may be composed of light bosons, ${m_b \sim 10^{-22}\,
\mathrm{eV}}$, with a de Broglie wavelength $\lambda \sim 1 \,\mathrm{kpc}$ in
typical galactic potentials. Such `fuzzy' dark matter (FDM) behaves like cold
dark matter (CDM) on much larger scales than the de Broglie wavelength, but may
resolve some of the challenges faced by CDM in explaining the properties of
galaxies on small scales ($\lesssim 10\,\mathrm{kpc}$). Because of its wave
nature, FDM exhibits stochastic density fluctuations on the scale of the de
Broglie wavelength that never damp. The gravitational field from these
fluctuations scatters stars and black holes, causing their orbits to diffuse
through phase space. We show that this relaxation process can be analyzed
quantitatively with the same tools used to analyze classical two-body
relaxation in an $N$-body system, and can be described by treating the FDM
fluctuations as quasiparticles, with effective mass $\sim 10^7 M_\odot
{(1\,\mathrm{kpc}/r)}^2{(10^{-22}\,\mathrm{eV}/m_b)}^3$ in a galaxy with a
constant circular speed of $200\,\mathrm{kms}$. This novel relaxation mechanism
may stall the inspiral of supermassive black holes or globular clusters due to
dynamical friction at radii of a few hundred pc, and can heat and expand the
central regions of galaxies. These processes can be used to constrain the mass
of the light bosons that might comprise FDM.
