Resonance photon generation in a vibrating cavity

The problem of photon creation from vacuum due to the non-stationary Casimir effect in an ideal one-dimensional Fabry-Perot cavity with vibrating walls is solved in the resonance case, when the frequency of vibrations is close to the frequency of some unperturbed electromagnetic mode: , , ( is the mean distance between the walls). An explicit analytical expression for the total energy in all the modes shows an exponential growth if is less than the dimensionless amplitude of vibrations , the increment being proportional to . The rate of photon generation from vacuum in the th mode goes asymptotically to a constant value , the numbers of photons in the modes with indices being the integrals of motion. The total number of photons in all the modes is proportional to in the short-time and in the long-time limits. In the case of strong detuning the total energy and the total number of photons generated from vacuum oscillate with the amplitudes decreasing as for . The special cases of p = 1 and p = 2 are studied in detail.