  We consider Landau damping of elementary excitations in Bose-Einstein
condensates (BECs) with dipolar interactions. We discuss quantum and
quasi-classical regimes of Landau damping. We use a generalized wave-kinetic
description of BECs which, apart from the long range dipolar interactions, also
takes into account the quantum fluctuations and the finite energy corrections
to short-range interactions. Such a description is therefore more general than
the usual mean field approximation. The present wave-kinetic approach is well
suited for the study of kinetic effects in BECs, such as those associated with
Landau damping, atom trapping and turbulent diffusion. The inclusion of quantum
fluctuations and energy corrections change the dispersion relation and the
damping rates, leading to possible experimental signatures of these effects.
  Quantum Landau damping is described with generality, and particular examples
of dipole condensates in two and three dimensions are studied. The occurrence
of roton-maxon configurations, and their relevance to Landau damping is also
considered in detail, as well as the changes introduced by the three different
processes, associated with dipolar interactions, quantum fluctuations and
finite energy range collisions. The present approach is mainly based on a
linear perturbative procedure, but the nonlinear regime of Landau damping,
which includes atom trapping and atom diffusion, is also briefly discussed.
