Fermion Particle Production in Dynamical Casimir Effect in a Three Dimensional Box

TL;DR

This study explores fermion creation inside a three-dimensional box with oscillating walls, deriving the particle production rate and energy using the dynamical Casimir effect and Bogoliubov transformations.

Contribution

It provides a detailed analysis of fermion particle production in a 3D cavity with dynamic boundaries, including explicit formulas for particle number and energy.

Findings

Derived Bogoliubov coefficients for fermion modes

Obtained expression for mean number of created fermions

Analyzed parametric resonance conditions

Abstract

In this paper we investigate the problem of fermion creation inside a three dimensional box. We present an appropriate wave function which satisfies the Dirac equation in this geometry with MIT bag model boundary condition. We consider walls of the box to have dynamic and introduce the time evolution of the quantized field by expanding it over the 'instantaneous basis'. We explain how we can obtain the average number of particles created. In this regard we find the Bogliubove coefficients. We consider an oscillation and determine the coupling conditions between different modes that can be satisfied depending on the cavity's spectrum. Assuming the parametric resonance case we obtain an expression for the mean number of created fermions in each mode of an oscillation and their dynamical Casimir energy.