  Motivated by trapping and cooling experiments with non-spherical
nanoparticles, we discuss how their combined rotational and translational
quantum state is affected by the interaction with a gaseous environment. Based
on the quantum master equation in terms of orientation-dependent scattering
amplitudes, we evaluate the localization rate for gas collisions off an
anisotropic van der Waals-type potential and for photon scattering off an
anisotropic dielectric. We also show how pure angular momentum diffusion arises
from these open quantum dynamics in the limit of weak anisotropies.
