Modified semiclassical approximation for trapped Bose gases

Abstract

A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The results of the modified approach are shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. Effective thermodynamic limit is defined for any confining dimension. The behaviour of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed.

Revtex file, 13 pages

References in corpus (7)

• Theory of the Weakly Interacting Bose Gas
• Physics with Coherent Matter Waves
• Condensate fluctuations of a trapped, ideal Bose gas
• Principal problems in Bose-Einstein condensation of dilute gases
• Low-dimensional Bose gases
• Statistical Green's Functions
• Dimensional and Temperature Crossover in Trapped Bose Gases

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