Quantum dissipative effects for a real scalar field coupled to a time-dependent Dirichlet surface in d+1 dimensions

TL;DR

This paper investigates the dynamical Casimir effect for a scalar field with a moving boundary, deriving pair creation probabilities and analyzing effects of dimensionality and non-linearities up to fourth order.

Contribution

It provides a perturbative framework for calculating pair creation due to a time-dependent boundary in arbitrary dimensions, including non-linear effects up to fourth order.

Findings

Derived general expressions for pair creation probability.

Analyzed impact of space-time dimensionality.

Explored non-linear effects up to fourth order.

Abstract

We study the Dynamical Casimir Effect (DCE) for a real scalar field $\varphi$ in $d+1$ dimensions, in the presence of a mirror that imposes Dirichlet boundary conditions and undergoes time-dependent motion or deformation. Using a perturbative approach, we expand in powers of the deviation of the mirror's surface $\Sigma$ from a hyperplane, up to fourth order. General expressions for the probability of pair creation induced by motion are derived, and we analyze the impact of space-time dimensionality as well as of the non-linear effects introduced by the fourth-order terms.