Repulsive Casimir forces at quantum criticality

TL;DR

This paper investigates the Casimir effect near a quantum critical point in a mean-field Bose gas, revealing that the force is generally repulsive and decays with distance in a non-universal manner.

Contribution

It provides an exact analysis of the Casimir force at quantum criticality in a mean-field Bose gas, highlighting its generic repulsive nature and decay behavior.

Findings

Casimir force is generally repulsive near quantum criticality.

Force decays algebraically or exponentially with non-universal amplitude.

Analysis is exact within the specified regime.

Abstract

We study the Casimir effect in the vicinity of a quantum critical point. As a prototypical system we analyze the $d$-dimensional imperfect (mean-field) Bose gas enclosed in a slab of extension $L^{d-1}\times D$ and subject to periodic boundary conditions. The thermodynamic state is adjusted so that $L\gg\lambda\gg D\gg\l_{mic}$, where $\lambda\sim T^{-1/2}$ is the thermal de Broglie length, and $l_{mic}$ denotes microscopic lengthscales. Our exact analysis indicates that the Casimir force in the above specified regime is generically repulsive and decays either algebraically or exponentially, with a non-universal amplitude.