Dynamical Casimir effect for a massless scalar field between two concentric spherical shells

TL;DR

This paper investigates the dynamical Casimir effect for a massless scalar field confined between two concentric spherical shells, deriving general formulas for particle creation and analyzing specific oscillation modes.

Contribution

It provides a general expression for particle creation in spherical geometry and compares results with plane geometry, using two different computational methods.

Findings

Derived a general formula for particle creation for arbitrary shell motion.

Analyzed particle production for breathing modes with different oscillation phases.

Compared spherical and planar geometries, highlighting differences in particle generation.

Abstract

In this work we consider the dynamical Casimir effect for a massless scalar field -- under Dirichlet boundary conditions -- between two concentric spherical shells. We obtain a general expression for the average number of particle creation, for an arbitrary law of radial motion of the spherical shells, using two distinct methods: by computing the density operator of the system and by calculating the Bogoliubov coefficients. We apply our general expression to breathing modes: when only one of the shells oscillates and when both shells oscillate in or out of phase. We also analyze the number of particle production and compare it with the results for the case of plane geometry.