Classical and quantum field theory in a box with moving boundaries: A numerical study of the dynamical Casimir effect

We present a detailed description of a quantum scalar field theory within a flat spacetime confined to a cavity with perfectly reflecting moving boundaries. Moreover, we establish an equivalence between this time-dependent setting and a field theory on an acoustic metric with static Dirichlet boundary conditions. We discuss the classical and quantum aspects of the theory from the latter perspective, accompanied by the introduction of novel numerical techniques designed for the (nonperturbative) computation of particle production attributed to the dynamical Casimir effect, applicable to arbitrary boundary trajectories. As an illustrative example of these methodologies, we compute the particle production for a massless field in $1+1$ dimensions. Notably, our approaches readily extend to encompass scenarios involving massive fields and higher dimensions.