Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

TL;DR

This paper calculates the quantum fluctuation-induced Casimir energy and pressure in a zero-temperature dilute Bose-Einstein condensate confined in a three-dimensional rectangular cavity, including higher-order Bogoliubov corrections.

Contribution

It extends previous work by deriving the Casimir effects for BECs in arbitrary rectangular geometries with periodic boundary conditions, incorporating finite-size and higher-order corrections.

Findings

Derived the Casimir energy for a BEC in a rectangular cavity.

Obtained the Casimir pressure including finite-size effects.

Identified the leading order as a massless scalar field with sound velocity.

Abstract

The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force) was previously calculated for the perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to {\it quantum} fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections which we refer to as Bogoliubov corrections. The leading order term is identified as the Casimir energy of a massless scalar field moving with wave velocity equal to the speed of sound in the BEC. We then obtain the leading order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary lengths and obtain the finite-size correction to the parallel plate scenario.