  In higher Landau levels ($N>1$), the ground state of the two-dimensional
electron gas in a strong perpendicular magnetic field evolves from a Wigner
crystal for small filling $\nu $ of the partially filled Landau level, into a
succession of bubble states with increasing number of guiding centers per
bubble as $\nu $ increases, to a modulated stripe state near $\nu =0.5$. In
this work, we compute the frequency-dependent longitudinal conductivity $%
\sigma_{xx}(\omega) $ of the Wigner and bubble crystal states in the presence
of disorder. We apply an elastic theory to the crystal states which is
characterized by a shear and a bulk modulus. We obtain both moduli from the
microscopic time-dependent Hartree-Fock approximation. We then use the replica
and Gaussian variational methods to handle the effects of disorder. Within the
semiclassical approximation we get the dynamical conductivity as well as the
pinning frequency as functions of the Landau level filling factor and compare
our results with recent microwave experiments.
