  We develop a classical microscopic model of a dielectric. The model features
nonlinear interaction terms between polarizable dipoles and lattice vibrations.
The lattice vibrations are found to act as a pseudo-reservoir, giving broadband
absorption of electromagnetic radiation without the addition of damping terms
in the dynamics. The effective permittivity is calculated using a perturbative
iteration method and is found to have the form associated with real
dielectrics. Spatial dispersion is naturally included in the model and we also
calculate the wavevector dependence of the permittivity.
