Quantum radiation force on a moving mirror with Dirichlet and Neumann boundary conditions at vacuum, finite temperature and coherent states

TL;DR

This paper derives exact formulas for the quantum radiation force on a moving mirror with different boundary conditions under various initial states, revealing equivalence in certain relativistic cases and confirming known results in the nonrelativistic limit.

Contribution

It provides exact expressions for the energy density and radiation force for Dirichlet and Neumann boundary conditions across different quantum states, including vacuum, thermal, and coherent states.

Findings

Dirichlet and Neumann conditions yield the same force under relativistic motion for time-translation invariant states.

Derived exact formulas for energy density and radiation force in various quantum states.

Results align with existing literature in the nonrelativistic limit.

Abstract

We consider a real massless scalar field in a two-dimensional spacetime, satisfying Dirichlet or Neumann boundary condition at the instantaneous position of a moving boundary. For a relativistic law of motion, we show that Dirichlet and Neumann boundary conditions yield the same radiation force on a moving mirror when the initial field state is invariant under time translations. We obtain the exact formulas for the energy density of the field and the radiation force on the boundary for vacuum, thermal and coherent state. In the nonrelativistic limit, our results coincide with those found in the literature.