  We adopt an open quantum system approach to study the effects of the
back-reaction from a quantum field onto the dynamics of a moving mirror. We
describe the coupling between the mirror and the field by using a microscopic
model from which the dielectric response of the mirror is obtained from first
principles. Using second-order perturbation theory, we derive the master
equation governing the mechanical motion of the mirror. Our analysis reveals
that the mirror experiences coloured noise and non-local dissipation, which
originate from the emission of particle pairs via the dynamical Casimir effect.
We show that the noise and dissipation kernels, that enter in the definition of
the time-dependent coefficients of the master equation, are related by
fluctuation-dissipation relations.
