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

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 being perturbed by the moving mirror, never meets this mirror in motion again, which allows us to exclude this effect of reinteraction on the particle creation process. Then, we describe the creation of particles with energies above ℏω0, due only to the relativistic aspect of the mirror’s velocity (and these particles form what we call relativistic bands). Thus, we analyze the formation of these relativistic bands in a discrete spectrum of created particles.