The imperfect Bose gas in d dimensions: critical behavior and Casimir forces

TL;DR

This paper provides an exact analytical study of the critical behavior and Casimir forces in a d-dimensional imperfect Bose gas confined in a slit geometry, revealing universal properties and scaling functions across different dimensions.

Contribution

It identifies the bulk universality class as the classical d-dimensional spherical model and derives the universal Casimir amplitudes and scaling functions for the system.

Findings

Casimir force decays exponentially above T_c with correlation length

At T_c and below T_c, decay is algebraic and governed by universal amplitudes

Scaling functions are monotonic for 2<d<4 and constant for d>4 at T≤T_c

Abstract

We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at Bose-Einstein condensation and identify the bulk universality class to be the one of the classical d-dimensional spherical model. Subsequently we consider finite slit width D and analyze the excess surface free energy and the related Casimir force acting between the slit boundaries. Above the bulk condensation temperature (T>T_c) the Casimir force decays exponentially as a function of D with the bulk correlation length determining the relevant length scale. For T=T_c and for T<T_c its decay is algebraic. The magnitude of the Casimir forces at T_c and for T<T_c is governed by the universal Casimir amplitudes. We extract the relevant values for different d and compute the scaling functions describing the crossover between the critical and low-temperature asymptotics of the Casimir force. The scaling function is monotonous at any d\in (2,4) and becomes constant for d>4 and T\leq T_c.