Critical Casimir force in the superfluid phase: effect of fluctuations

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 $T\lesssim 2.13\text{K}$.

The term $\frac{1}{4b}{\xi }_0^4{k}_B{T}_{\lambda }$ at the Fig.2-caption in the published version should be read as $\frac{1}{4b{\xi }_0^4{k}_B{T}_{\lambda }}$

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• Critical Casimir Effect: Exact Results
• The thermodynamic Casimir effect in the neighbourhood of the lambda-transition: A Monte Carlo study of an improved three dimensional lattice model
• Large-$n$ approach to thermodynamic Casimir effects in slabs with free surfaces
• Crossover from Goldstone to critical fluctuations: Casimir forces in confined O$(\mathbf{n})$ symmetric systems
• Crossover from low-temperature to high-temperature fluctuations. I. Thermodynamic Casimir forces of isotropic systems
• Crossover from low-temperature to high-temperature fluctuations. II. Nonuniversal thermodynamic Casimir forces of anisotropic systems
• Pronounced minimum of the thermodynamic Casimir forces of O($\mathbf{n}$) symmetric film systems: Analytic theory
• Exact solution for the order parameter profiles and the Casimir force in ${}^4$He superfluid films in an effective field theory
• Casimir effect for a Bose-Einstein condensate inside a cylindrical tube