Dynamical Casimir effect with Dirichlet and Neumann boundary conditions

TL;DR

This paper investigates the dynamical Casimir effect by deriving the radiation pressure force on a moving boundary in 1+1 dimensions, comparing Dirichlet and Neumann boundary conditions, and analyzing the influence of different quantum states.

Contribution

It provides a detailed derivation of the radiation pressure force for both Dirichlet and Neumann boundary conditions and explores how quantum states affect the results.

Findings

For time-translation invariant states, Dirichlet and Neumann BC yield identical forces.

Thermal states produce the same force for both BC types.

Coherent states lead to different forces depending on boundary conditions.

Abstract

We derive the radiation pressure force on a non-relativistic moving plate in 1+1 dimensions. We assume that a massless scalar field satisfies either Dirichlet or Neumann boundary conditions (BC) at the instantaneous position of the plate. We show that when the state of the field is invariant under time translations, the results derived for Dirichlet and Neumann BC are equal. We discuss the force for a thermal field state as an example for this case. On the other hand, a coherent state introduces a phase reference, and the two types of BC lead to different results.