Casimir force induced by imperfect Bose gas

TL;DR

This paper investigates the Casimir force in an imperfect Bose gas, revealing exponential decay in the one-phase region and long-range power-law decay near the Bose-Einstein condensation point, with critical behavior differing from perfect gases.

Contribution

It provides a detailed analysis of the Casimir effect in an imperfect Bose gas, highlighting the impact of interactions on decay laws and critical exponents.

Findings

Force decays exponentially in the one-phase region

Decay length diverges with critical exponent 1 near BEC point

In the two-phase region, the force follows a D^{-3} power law

Abstract

We present a study of the Casimir effect in an imperfect (mean-field) Bose gas contained between two infinite parallel plane walls. The derivation of the Casimir force follows from the calculation of the excess grand canonical free energy density under periodic, Dirichlet, and Neumann boundary conditions with the use of the steepest descent method. In the one-phase region the force decays exponentially fast when distance $D$ between the walls tends to infinity. When Bose-Einstein condensation point is approached the decay length in the exponential law diverges with critical exponent $\nu_{IMP}=1$, which differs from the perfect gas case where $\nu_{P}=1/2$. In the two-phase region the Casimir force is long-range, and decays following the power law $D^{-3}$, with the same amplitude as in the perfect gas.