Quantum radiation reaction force on a one-dimensional cavity with two relativistic moving mirrors

TL;DR

This paper derives exact formulas for the energy density and quantum radiation reaction force on a two-dimensional cavity with two relativistically moving mirrors, extending previous results to arbitrary motions.

Contribution

It provides a general analytical framework for calculating quantum forces in a cavity with two moving mirrors at relativistic speeds, which was not previously available.

Findings

Formulas for energy density and quantum force for arbitrary mirror motion

Results reduce to known cases for single moving boundary or non-relativistic speeds

Extends previous work to relativistic and arbitrary boundary motions

Abstract

We consider a real massless scalar field inside a cavity with two moving mirrors in a two-dimensional spacetime, satisfying Dirichlet boundary condition at the instantaneous position of the boundaries, for arbitrary and relativistic laws of motion. Considering vacuum as the initial field state, we obtain formulas for the exact value of the energy density of the field and the quantum force acting on the boundaries, which extend results found in previous papers. For the particular cases of a cavity with just one moving boundary, non-relativistic velocities, or in the limit of infinity length of the cavity (a single mirror), our results coincide with those found in the literature.