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 Δvar/D for large D. The amplitude Δvar is a non-universal function of two scaling variables λ/ξ and D/ξ, where λ is the thermal de Broglie wavelength and ξ 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 Δvar retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form , where L is the linear size of the wall.