Radiation modes of a cavity with a resonantly oscillating boundary

Abstract

We present exact analytic solutions to describe the quantum dynamics of the radiation modes in a one-dimensional cavity vibrating at any one of its resonance frequencies. For a cavity vibrating at its $m\mathrm{th} (m>~2)$ eigenfrequency, m traveling wave packets emerge in the finite part of the field energy density and their amplitudes grow while their widths shrink in time, representing a large concentration of energy. There also exists a ``sub-Casimir'' region where the energy density equals ${m}^{2}$ times the static Casimir energy density.