On the Casimir interaction between holes

TL;DR

This paper investigates the long-distance Casimir-like attractive force between holes in a plate caused by a scalar field, revealing universal 1/r^7 behavior for large separations and extending analysis to slits.

Contribution

It introduces a non-local field theory framework to compute the interaction between holes and demonstrates the universal 1/r^7 decay law at large distances.

Findings

Interaction energy scales as 1/r^7 for holes at large separation.

Charges associated with holes are computed explicitly.

Interaction between slits decays as 1/r^6.

Abstract

We study the leading long-distance attractive force between two holes in a plate arising from a scalar field with Dirichlet boundary conditions on the plate. We use a formalism in which the interaction is governed by a non-local field theory which lives on the two holes. The interaction energy is proportional to Q_1 Q_2/r^7 at large separation r, where Q_1 and Q_2 are certain charges associated with the holes. We compute these charges for round and rectangular holes. We show that the 1/r^7 behavior is universal for separations large compared to the linear dimensions of the holes, irrespective of the spin or interactions of the bosonic field. We also study the interaction between two long thin slits, for which the energy falls off as 1/r^6.