Parametric resonance in a vibrating cavity

Abstract

We present the study of parametric resonance in a one-dimensional cavity based on the analysis of classical optical paths. The recursive formulas for field energy are given. We separate the mechanism of particle production and the resonance amplification of radiation. The production of photons is a purely quantum effect described in terms of quantum anomalies in recursive formulas. The resonance enhancement is a classical phenomenon of focusing and amplifying beams of photons due to Döppler effect.

Fifty Years of the Dynamical Casimir Effect

“…, with the same function g(ξ) (15). It was shown in [68,[85][86][87] that, for q ≥ 2, the energy density grows exponentially in the form of q traveling wave packets, which become narrower and higher as time increases. The total energy also grows exponentially.…”

An optical approach to the dynamical Casimir effect

“…n (τ ) are to be determined from the retardation relations T ⋆ n (τ ) + L(T ⋆ n (τ )) = T n (τ ). The parametric resonance is related to the existence of periodic particle trajectories [8,11]. Each periodic trajectory obeys a following condition (for any non-negative integer n):…”

“…It is usually assumed that T /2 refers to the length of the static cavity, so that T /2 ≡ L ≡ L(0). The crucial characteristic of a particle trajectory is the cumulative Doppler factor [8]:…”

“…Another idea based on a concept of renormalization group was proposed in [6,7]. Our suggestion [8] is to trace the evolution of the quantum fields in a vibrating cavity system following classical optical paths. It is related to the iteration procedure described in [9] and techniques developed for classical field theory in [10] and [11].…”

“…In the present paper, we apply our technique [8] to examine cavities with various kinds of their motion and different types of boundary conditions. The calculations are involved in determining the essential physical outcome.…”