Resonance photon generation in a vibrating cavity

The problem of photon creation from vacuum due to the non-stationary Casimi r effect in an ideal one-dimensional Fabry-Perot cavity with vibrating wall s is solved in the resonance case, when the frequency of vibrations is clos e to the frequency of some unperturbed electromagnetic mode: omega(w) = p(p i c/L-0)(1 + delta), \delta\ << 1, p = 1, 2, ... (L-0 is the mean distance between the walls). An explicit analytical expression for the total energy in all the modes shows an exponential growth if \delta\ is less than the di mensionless amplitude of vibrations epsilon << 1, the increment being propo rtional to p root epsilon(2)-delta(2). The rate of photon generation from v acuum in the (j + ps)th mode goes asymptotically to a constant value cp(2) sin(2) (pi j/p)root epsilon(2) - delta(2)/[pi L-0(j + ps)], the numbers of photons in the modes with indices p, 2p, 3p .... being the integrals of mot ion. The total number of photons in all the modes is proportional to p(3)(e psilon(2) - delta(2))t(2) in the short-time and in the long-time limits. In the case of strong detuning \delta\ > epsilon the total energy and the tot al number of photons generated from vacuum oscillate with the amplitudes de creasing as (epsilon/delta)(2) for epsilon << \delta\. The special cases of p = 1 and p = 2 are studied in detail.