Exact solution for the energy density inside a one-dimensional non-static cavity with an arbitrary initial field state

TL;DR

This paper derives an exact solution for the energy density of a massless scalar field in a two-dimensional non-static cavity with arbitrary initial states, extending previous work to include various boundary conditions and non-diagonal states.

Contribution

It generalizes existing solutions to include Neumann and Dirichlet boundary conditions and non-diagonal initial states like coherent and Schrödinger cat states.

Findings

Provides exact energy density solutions for various initial states.

Extends previous models to non-static cavities with different boundary conditions.

Analyzes vacuum, thermal, and non-diagonal states within the framework.

Abstract

We study the exact solution for the energy density of a real massless scalar field in a two-dimensional spacetime, inside a non-static cavity with an arbitrary initial field state, taking into account the Neumann and Dirichlet boundary conditions. This work generalizes the exact solution proposed by Cole and Schieve in the context of the Dirichlet boundary condition and vacuum as the initial state. We investigate diagonal states, examining the vacuum and thermal field as particular cases. We also study non-diagonal initial field states, taking as examples the coherent and Schrodinger cat states.