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.

Motivated by recent parity violating electron scattering experiments, we compute the Neutron Skin Thickness (NST) of nuclei modelled as (quantized) Skyrmions, the topological solitons of the Skyrme model. We show how in a certain approximation, the result for the NST is oblivious to the fine details of the (generally very complicated) quantum state of the soliton and only depends on the total baryon number and the isospin number. Moreover, in the leading order, the linear dependence on the asymmetry parameter is recovered, as expected both from experimental data and other models of nuclei such as the liquid drop model.