Fermionic dynamical Casimir effect: Magnus expansion

TL;DR

This paper investigates the fermionic dynamical Casimir effect in a 1+1 dimensional system with oscillating boundaries, using a Magnus expansion to analyze pair creation and transition amplitudes.

Contribution

It introduces a Magnus expansion approach to compute vacuum decay and pair creation amplitudes in a fermionic system with moving boundaries, providing explicit unitary transformations.

Findings

Derived multipair creation amplitudes.

Provided corrections to single-pair creation amplitudes.

Obtained an explicit, unitary Bogoliubov transformation.

Abstract

We study pair creation out of the vacuum, for a system consisting of a massive Dirac field in $1+1$ dimensions, contained between a pair of perfectly reflecting boundaries, one of them oscillating. After analyzing some general properties of the vacuum-decay process, we evaluate the corresponding transition amplitude in a Magnus expansion of the S-matrix. We show how this yields, besides the single-pair creation amplitude, multipair ones, as well as corrections to the single pair amplitude. We also apply it to obtain an approximate, yet explicitly unitary expression for the Bogoliubov transformation between the in and out Fock spaces.