  Theory of linear microwave response of thin films of type-II superconductors
in the mixed state is developed taking into account random spatial fluctuations
of the parameters of the system, such as the order parameter, diffusion
coefficient, or film thickness. In the regime of collective pinning the
microwave response of the system exhibits strong frequency dispersion, arising
from nonequilibrium vortex core quasiparticles. The corresponding contribution
to the ac conductivity is controlled by the inelastic relaxation time, and may
exceed the usual Bardeen-Stephen conductivity. It is caused by the Debye-type
inelastic relaxation. Debye mechanism of microwave losses may be responsible
for strong effects of electromagnetic noise upon dc conductivity in the mixed
state at low temperatures.
