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 nω 1 (n = 1, 2, 3, ...) which is a generalization of other works considering only 2ω 1 , where ω 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. 03.65.Ca, 42.50.Dv

Numerical approach to the dynamical Casimir effect

“…The numerical results are entirely in agreement with the analytical predictions derived in [6,8] demonstrating that the numerical simulations are reliable and the method introduced is appropriate to study the dynamical Casimir effect fully numerically.…”

“…The numerically calculated spectra for times t = 25 shown in Fig. 2 are well fitted by the analytical expression N k (t) = (2n−k)k(10 −3 πt) 2 /4 for k < 2n and N k (t) = 0 otherwise [6], predicting a parabolic shape of the particle spectrum. More quantitatively, for n = 2, for instance, the predicted values N 1 (t = 25) = N 3 (t = 25) ∼ 4.63 × 10 −3 , N 2 (t = 25) = 6.17 × 10 −3 agree well with the values N 1 (t = 25) = 4.62 × 10 −3 , N 2 (t = 25) = 6.14 × 10 −3 and N 3 (t = 25) = 4.59 × 10 −3 obtained from the numerical simulations with k max = 50.…”

“…Particle creation in one-dimensional vibrating cavities has been studied in numerous works [3,4,5,6,7,8,9,10,11]. When considering small amplitude oscillations, analytical results can be deduced showing that under resonance conditions the particle occupation numbers increase quadratically in time.…”

“…(19), (20)] can be introduced in the following way: Define an operatorb n (t) viab n (t) :=Û † (t, 0)â nÛ (t, 0) withâ n being the annihilation operator corresponding to the initial state [Eq. (6)…”

Cosmological Particle Creation and Dynamical Casimir Effect

“…The corresponding problem for a sphere expanding in the four-dimensional spacetime with constant acceleration is investigated by Frolov and Serebriany [6,7] in the perfectly reflecting case and by Frolov and Singh [8] for semi-transparent boundaries. For more general cases of motion by vibrating cavities the problem of particle and energy creation is considered on the base of various perturbation methods [9,10,11,12,13,14,15,16](for more complete list of references see [16]). It have been shown that a gradual accumulation of small changes in the quantum state of the field could result in a significant observable effect.…”