Statistical mechanics of an ideal Bose gas in a confined geometry

Abstract

We study the behaviour of an ideal non-relativistic Bose gas in a three-dimensional space where one of the dimensions is compactified to form a circle. In this case there is no phase transition like that for the case of an infinite volume, nevertheless Bose-Einstein condensation signified by a sudden buildup of particles in the ground state can occur. We use the grand canonical ensemble to study this problem. In particular, the specific heat is evaluated numerically, as well as analytically in certain limits. We show analytically how the familiar result for the specific heat is recovered as we let the size of the circle become large so that the infinite volume limit is approached. We also examine in detail the behaviour of the chemical potential and establish the precise manner in which it approaches zero as the volume becomes large.

13 pages, 2 eps figures, revtex4

References in corpus (6)

• Bose-Einstein condensation in a circular waveguide
• Quantum many particle systems in ring-shaped optical lattices
• Bose-Einstein Condensation on inhomogeneous complex networks
• Bose-Einstein Condensation on inhomogeneous networks: mesoscopic aspects versus thermodynamic limit
• Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks
• zeta-function regularization and the interacting Bose gas at low temperature

Cited by in corpus (2)

• Finite-size effects on the Bose-Einstein condensation critical temperature in a harmonic trap
• Bose-Einstein condensation in the three-sphere and the infinite slab: analytical results