Variance of the Casimir force in an ideal Bose gas

Abstract

We consider an ideal Bose gas enclosed in a $d$-dimensional slab of thickness $D$. Using the grand canonical ensemble we calculate the variance of the thermal Casimir force acting on the slab's walls. The variance evaluated per unit wall area is shown to decay like ${\Delta }_{var}/D$ for large $D$. The amplitude ${\Delta }_{var}$ is a non-universal function of two scaling variables $\lambda /\xi$ and $D/\xi$, where $\lambda$ is the thermal de Broglie wavelength and $\xi$ is the bulk correlation length. It can be expressed via the bulk pressure, the Casimir force per unit wall area, and its derivative with respect to chemical potential. For thermodynamic states corresponding to the presence of the Bose-Einstein condensate the amplitude ${\Delta }_{var}$ retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form $(D/L{)}^{\frac{d-1}{2}}(D/\lambda {)}^{d/2}$, where $L$ is the linear size of the wall.

9 pages, no figures

References in corpus (3)

• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Relation between the thermodynamic Casimir effect in Bose-gas slabs and critical Casimir forces
• Non-universal Casimir forces at Bose-Einstein condensation of an ideal gas: effect of Dirichlet boundary conditions

Cited by in corpus (2)

• Critical Casimir Effect: Exact Results
• Effective binding potential from Casimir interactions: the case of the Bose gas