Relativistic bands in the discrete spectrum of created particles in an oscillating cavity

Abstract

We investigate the dynamical Casimir effect for a one-dimensional resonant cavity, with one oscillating mirror. Specifically, we study the discrete spectrum of created particles in a region of frequencies above the oscillation frequency ω0 of the mirror. We focus our investigation on an oscillation time equal to 2L0/c, where L0 is the initial and final length of the cavity, and c is the speed of light. For this oscillation duration, a field mode, after perturbed by the moving mirror, never meets this mirror in motion again, which allows us to exclude this effect of re-interaction on the particle creation process. Then, we describe the evolution of the particle creation with frequencies above ω0 only as a function of the relativistic aspect of the mirror's velocity. In other words, we analyse the formation of relativistic bands in a discrete spectrum of created particles.