Non-superposition effects in the Dirichlet Casimir effect

TL;DR

This paper investigates how the Dirichlet Casimir effect deviates from superposition principles in multi-boundary systems across various dimensions, highlighting conditions under which these effects are negligible.

Contribution

It provides a theoretical analysis of non-superposition effects in the Dirichlet Casimir interaction, including general results and specific examples in multiple dimensions.

Findings

Non-superposition effects diminish when surface distances exceed their sizes.

Derived general results about the magnitude of non-superposition effects.

Analyzed examples in 1D, 2D, and 3D to illustrate the effects.

Abstract

We study non-superposition effects in the Dirichlet Casimir interaction energy for N boundaries in d spatial dimensions, quantifying its departure from the case of an interaction where a superposition principle is valid. We first derive some general results about those effects, and then show that they only become negligible when the distances between surfaces are larger than the sizes of each individual surface. We consider different examples in one, two and three spatial dimensions.