  We present a microscopic calculation of the energy dissipation in the core of
a vortex moving in a two-dimensional or layered superconductor in the
moderately clean regime. In this regime, the quasiclassical Bardeen--Stephen
result remains valid in spite of the strong correlations between the energy
levels. We find that the quasiclassical expression applies both in the limit of
fast vortex motion (with transitions between smeared levels) and in the limit
of slow vortex motion (with nearly adiabatic dynamics). This finding can be
related to the similar result known for the unitary random-matrix model.
