First- and Second-Order Forces in the Asymmetric Dynamical Casimir Effect for a Single δ − δ′ Mirror

Here, we consider an asymmetric δ−δ′ mirror undergoing time-dependent interactions with a massless scalar field in 1 + 1 dimensions. Using fluctuation-dissipation theory for a mirror in vacuum, we compute the force on a moving δ−δ′ mirror with time-dependent material properties. We investigate the first-order forces arising from the two distinct fluctuation sources and calculate the linear susceptibility in each case. We then plot the resulting forces. At the second order, we also find the independent contributions to the total force as well as the force that arises from the interference phenomena between the two fluctuation sources.