Production of photons by the parametric resonance in the dynamical Casimir effect

Abstract

We calculate the number of photons produced by the parametric resonance in a cavity with vibrating walls. We consider the case that the frequency of vibrating wall is $n{\omega }_1(n=1,2,3,...)$ which is a generalization of other works considering only $2{\omega }_1$, where ${\omega }_1$ is the fundamental-mode frequency of the electromagnetic field in the cavity. For the calculation of time-evolution of quantum fields, we introduce a new method which is borrowed from the time-dependent perturbation theory of the usual quantum mechanics. This perturbation method makes it possible to calculate the photon number for any $n$ and to observe clearly the effect of the parametric resonance.

15 pages, RevTeX, no figures

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