Casimir force between $\delta-\delta^{\prime}$ mirrors transparent at high frequencies

TL;DR

This paper introduces a modified $-^{}$ point interaction model for partially reflecting mirrors that achieves full transparency at high frequencies, and analyzes its impact on the Casimir force in a 1+1D scalar field.

Contribution

It proposes a new modified $-^{}$ model that allows for high-frequency transparency, improving the realism of Casimir force calculations.

Findings

The modified model achieves full transparency at high frequencies.

Comparison shows differences in Casimir force predictions with previous models.

Results suggest more accurate modeling of mirror transparency effects.

Abstract

We investigate, in the context of a real massless scalar field in $1+1$ dimensions, models of partially reflecting mirrors simulated by Dirac $\delta-\delta^{\prime}$ point interactions. In the literature, these models do not exhibit full transparency at high frequencies. In order to provide a more realistic feature for these models, we propose a modified $\delta-\delta^{\prime}$ point interaction that enables full transparency in the limit of high frequencies. Taking this modified $\delta-\delta^{\prime}$ model into account, we investigate the Casimir force, comparing our results with those found in the literature.