Critical Casimir force in the superfluid phase: effect of fluctuations

TL;DR

This paper investigates the critical Casimir force in superfluid helium films near the lambda transition, emphasizing the role of fluctuations and improving upon previous mean field results to reveal universal behavior.

Contribution

It introduces a perturbative approach to account for fluctuations, refining the mean field predictions of the Casimir force in superfluid helium.

Findings

Casimir scaling function approaches a universal constant below 2.13 K

Fluctuations significantly modify mean field results

Improved agreement with theoretical predictions

Abstract

We have considered the critical Casimir force on a $^4$He film below and above the bulk $\lambda$ point. We have explored the role of fluctuations around the mean field theory in a perturbative manner, and have substantially improved the mean field result of Zandi et al [Phys. Rev. E {\bf 76}, 030601(R) (2007)]. The Casimir scaling function obtained by us approaches a universal constant ($-\frac{\zeta(3)}{8\pi}$) for $T\lesssim 2.13~\text{K}$.