Dynamical Casimir effect for a massless scalar field between two concentric spherical shells with mixed boundary condictions

TL;DR

This paper investigates the dynamical Casimir effect for a massless scalar field between two concentric spherical shells with mixed boundary conditions, deriving a general particle creation formula and analyzing harmonic shell oscillations.

Contribution

It extends previous work by considering mixed boundary conditions and provides a general expression for particle creation with arbitrary shell motion.

Findings

Derived a general formula for particle creation with mixed boundary conditions.

Analyzed particle production during harmonic oscillations of the shells.

Compared results with Dirichlet-Dirichlet boundary conditions.

Abstract

We analyze the dynamical Casimir effect for a massless scalar field confined between two concentric spherical shells which impose on the field mixed boundary conditions. We thus complement a previous result [Phys. Rev. A \textbf{78}, 032521 (2008)], where the same problem was considered but in that case the field was submitted to a Dirichlet boundary condition in both moving spherical shells. A general expression for the average number of created particles is deduced for an arbitrary law of radial motion of the spherical shells. This expression is then applied to harmonic oscillations of the shells and the number of created particles is analyzed and compared with the results obtained under Dirichlet-Dirichlet boundary conditions.