Exponential Growth of the Energy of a Wave in a 1D Vibrating Cavity: Application to the Quantum Vacuum

The wave equation in a one--dimensional cavity is equivalent to the motion of massless particles in a two-dimensional space-time billiard. This allows us to consider, in a simple way, the case of a cavity with one or two oscillating walls. It is shown that a set of continuous families of frequencies of the oscillating walls leads to an exponential growth of the energy of a wave. For such cases, the wave energy is localized in narrow space regions moving at the wave velocity. As a consequence the electromagnetic vacuum fluctuations inside the cavity increase exponentially and the possibility to observe experimentally photon creation from the vacuum could be reconsidered.