Bose-Einstein Condensation on Product Manifolds

Abstract

We investigate the phenomenon of Bose-Einstein condensation on manifolds constructed as a product of a three-dimensional Euclidian space and a general smooth, compact $d$-dimensional manifold possibly with boundary. By using spectral $\zeta$-function methods, we are able to explicitly provide thermodynamical quantities like the critical temperature and the specific heat when the gas of bosons is confined, in the three-dimensional manifold, by the experimentally relevant anisotropic harmonic oscillator potential.

9 pages, LaTeX

References in corpus (15)

• Heat kernel expansion: user's manual
• Bose-Einstein condensation of atomic gases in a harmonic oscillator confining potential trap
• The critical temperature of a trapped, weakly interacting Bose gas
• A more accurate analysis of Bose-Einstein condensation in harmonic traps
• The Casimir Effect in the Presence of Compactified Universal Extra Dimensions
• The Casimir Force in Randall Sundrum Models
• Bose-Einstein Condensation in Anisotropic Harmonic Traps
• Maxwell's Demon at work: Two types of Bose condensate fluctuations in power-law traps
• The Casimir force on a piston in the spacetime with extra compactified dimensions
• Bose-Einstein condensation in arbitrarily shaped cavities
• Density of states for Bose-Einstein condensation in harmonic oscillator potentials
• Bose-Einstein condensation under external conditions
• Finite Temperature and Density Effects in Higher Dimensions with and without Compactifications
• Bose-Einstein condensation as symmetry breaking in compact curved spacetimes
• Applications of the Mellin-Barnes integral representation

Cited by in corpus (5)

• Finite temperature current densities and Bose-Einstein condensation in topologically nontrivial spaces
• Bose-Einstein condensation in the three-sphere and the infinite slab: analytical results
• Virial coefficients expressed by heat kernel coefficients
• Vacuum instability in Kaluza-Klein manifolds
• Heat Kernel Asymptotic Expansion on Unbounded Domains with Polynomially Confining Potentials