The dynamical Casimir effect for an oscillating dielectric model

Dynamical Casimir effects caused by a moving mirror and a varying dielectric medium are studied in the effective Hamiltonian approach. The explicit form of the effective Hamiltonian for the uniform, step-wise, and time-dependent dielectric model is derived in addition to that for the moving mirror model. The resonant properties of induced photons for both models are considered and it is found that in contrast to the moving mirror case, the inter-mode transition for the dielectric case is suppressed between the odd-odd levels and between the even-even levels. The effects of dissipation are also taken into account by the master equation. For numerical analyses, a convenient method to integrate the time evolution is proposed.