Number Fluctuation in an interacting trapped gas in one and two dimensions

Abstract

It is well-known that the number fluctuation in the grand canonical ensemble, which is directly proportional to the compressibility, diverges for an ideal bose gas as T -> 0. We show that this divergence is removed when the atoms interact in one dimension through an inverse square two-body interaction. In two dimensions, similar results are obtained using a self-consistent Thomas-Fermi (TF) model for a repulsive zero-range interaction. Both models may be mapped on to a system of non-interacting particles obeying the Haldane-Wu exclusion statistics. We also calculate the number fluctuation from the ground state of the gas in these interacting models, and compare the grand canonical results with those obtained from the canonical ensemble.

11 pages, 1 appendix, 3 figures. Submitted to J. Phys. B: Atomic, Molecular & Optical

References in corpus (3)

• Canonical Statistics of Trapped Ideal and Interacting Bose Gases
• Statistical Properties of Interacting Bose Gases in Quasi-2D Harmonic Traps
• Exclusion Statistics in a two-dimensional trapped Bose gas

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• Fluctuations of a weakly interacting Bose-Einstein condensate
• Anomalous fluctuations of two-dimensional Bose-Einstein condensates
• Exact ground state number fluctuations of trapped ideal and interacting fermions
• Number Fluctuation and the Fundamental Theorem of Arithmetic
• Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate
• The virial expansion of a classical interacting system
• Semi-classical and quantum description of an ideal Bose gas in a uniform gravitational field
• Condensate fluctuations in the dilute Bose gas