Resonant energy exchange between a moving boundary and radiation modes of a cavity

We discuss the dynamics of a quantum vacuum in a one-dimensional cavity formed by two ideal mirrors: one fixed, the other moving. A nonrelativistic equation of motion is found for the wall that self-consistently determines the wall position and the evolution of the quantum field. This equation is applied to a system with an external potential chosen so that the mirror oscillates at a resonant frequency of the cavity. It is found that this system has an evolutionary cycle during which energy is transferred back and forth between the cavity field and the wall. During the first and third phases of the cycle, energy is transferred from the wall to the cavity; wave packets form in the field as the wall motion decays. During the second and fourth phases, energy is transferred from the field to the wall. The wave packets disperse, providing an impetus for the waxing wall motion.