Dynamical Casimir effect with $\delta-\delta^{\prime}$ mirrors

TL;DR

This paper investigates the particle creation spectrum and rate due to a partially transparent, moving mirror modeled by a Dirac delta-delta' interaction, revealing that partial reflectivity can enhance particle production compared to perfect mirrors.

Contribution

It introduces a novel model using delta-delta' interactions to simulate partially transparent moving mirrors and derives the resulting particle creation spectrum and rate.

Findings

Partially reflecting mirrors can produce more particles than perfect ones.

Formulas recover known results for perfect mirrors in the appropriate limit.

The model provides a new way to analyze the dynamical Casimir effect with partial transparency.

Abstract

We calculate the spectrum and the total rate of created particles for a real massless scalar field in $1+1$ dimensions, in the presence of a partially transparent moving mirror simulated by a Dirac $\delta-\delta^{\prime}$ point interaction. We show that, for this model, a partially reflecting mirror can produce a larger number of particles in comparison with a perfect one. In the limit of a perfect mirror, our formulas recover those found in the literature for the particle creation by a moving mirror with a Robin boundary condition.