  The optical conductivity of charge carriers coupled to quantum phonons is
studied in the framework of the one-dimensional spinless Holstein model. For
one electron, variational diagonalisation yields exact results in the
thermodynamic limit, whereas at finite carrier density analytical
approximations based on previous work on single-particle spectral functions are
obtained. Particular emphasis is put on deviations from weak-coupling,
small-polaron or one-electron theories occurring at intermediate coupling
and/or finite carrier density. The analytical results are in surprisingly good
agreement with exact data, and exhibit the characteristic polaronic excitations
observed in experiments on manganites.
