Nonequilibrium backreaction on a moving charge and mirror in quantum fields

Backreaction on a nonrelativistic moving charge and mirror under the influence of quantum fields is studied. We employ the closed-time-path formalism to obtain the influence functional by tracing out quantum fields. The respective semiclassical Langevin equation is derived and can be used to describe the stochastic behavior on its mean trajectory with a self-consistent backreaction. In particular, when backreaction dissipation and fluctuations are taken into account, the corresponding fluctuation-dissipation theorem obtained from the first-principles derivation must be fulfilled. The implications of the results from solving the semiclassical Langevin equation are discussed.