Bubble-wall Casimir interaction in fermionic environments

TL;DR

This paper calculates the Casimir interaction energy mediated by massless fermions between a spherical defect and a flat barrier, revealing unique distance scaling behaviors and corrections to the proximity force approximation.

Contribution

It provides an exact integral formula for the fermionic Casimir energy and analyzes its asymptotic behaviors at different distances, highlighting differences from electromagnetic Casimir effects.

Findings

Fermionic Casimir energy scales as L^{-3} at large distances.

Short-distance energy matches proximity force approximation predictions.

Sub-leading correction at short distances is positive, unlike in electromagnetic cases.

Abstract

We consider the Casimir interaction, mediated by massless fermions, between a spherical defect and a flat potential barrier, assuming hard (bag-type) boundary conditions at both the barrier and the surface of the sphere. The computation of the quantum interaction energy is carried out using the multiple scattering approach, adapted here to the setup in question. We find an exact integral formula for the energy, from which we extract both the large and short distance asymptotic behaviour. At large distance the fermionic contribution is found to scale as $L^{-3}$, in contrast to that of electromagnetic vacuum fluctuations that, assuming perfectly conducting boundaries, scales as $L^{-4}$. At short distance, we compute the leading and sub-leading contribution to the vacuum energy. The leading one coincides with what it is expected from the proximity force approximation, while the sub-leading term gives, contrary to the electromagnetic case, a positive correction to the proximity force result.