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arXiv:quant-ph/0211189 · Physical Review A

Comment on “Bose-Einstein condensation in low-dimensional traps”

Wu-Sheng Dai, Mi Xie

Published Feb 14, 2003• 8 citations
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Abstract

We show that the critical temperature of a one-dimensional gas confined by a power-law potential should be lower than that in the paper of Bagnato and Kleppner [Phys. Rev. A 44, 7439 (1991)]. Moreover, a sketch of the critical temperature is given in greater detail.
DOI
10.1103/physreva.67.027601

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Reply to “Comment on ‘Bose-Einstein condensation with a finite number of particles in a power-law trap’ ”

Amine Jaouadi, Mourad Telmini, Éric Charron

In this Reply to Comment we show that the criticisms raised by J. Noronha are based on a misapplication of the model we have proposed in A. Jaouadi, M. Telmini, and E. Charron [Phys. Rev. A 83, 023616 (2011)]. Here we explicitly discuss the range of validity of the approximations underlying our analytical model. We also show that the discrepancies pointed out for very small atom numbers and for very anisotropic traps are not surprising since these conditions exceed the range of validity of the model.

Physical Review A•Jul 16, 2015•2 citations

Reply to "Comment on 'Bose-Einstein condensation with a finite number of particles in a power-law trap'"

Amine Jaouadi, Mourad Telmini, Éric Charron

In this reply we show that the criticisms raised by J. Noronha are based on a misapplication of the model we have proposed in [A. Jaouadi, M. Telmini, E. Charron, Phys. Rev. A 83, 023616 (2011)]. Here we explicitly discuss the range of validity of the approximations underlying our analytical model. We also show that the discrepancies pointed out for very small atom numbers and for very anisotropic traps are not surprising since these conditions exceed the range of validity of the model.

arXiv:1507.02016•Jul 8, 2015•0 citations
In Jaouadi et al. [Phys. Rev. A 83, 023616 (2011)] the authors derive an analytical finite-size expansion for the Bose-Einstein condensation critical temperature of an ideal Bose gas in a generic power-law trap. In the case of a harmonic trap, this expansion adds higher-order terms to the well-known first-order correction. We point out a delicate point in connection to these results, showing that the claims of Jaouadi et al. should be treated with caution. In particular, for a harmonic trap, the given expansion yields results that, depending on what is considered to be the critical temperature of the finite system, do not generally improve on the established first-order correction. For some nonharmonic traps, the results differ at first order from other results in the literature.
The critical temperature for Bose-Einstein condensation, ground-state fraction, and heat capacity of an ideal gas of Bose particles that are confined by an n-dimensional generic power-law potential trap are derived. The conditions for Bose-Einstein condensation and the discontinuous conditions of the heat capacity at critical temperature are obtained. All these quantities and conditions are found to vary markedly with the dimensionality of space, characteristics of particles, and shape of the external potential. The results obtained here are universal.
In this Reply to Comment we show that the criticisms raised by J. Noronha are based on a misapplication of the model we have proposed in A. Jaouadi, M. Telmini, and E. Charron [Phys. Rev. A 83, 023616 (2011)]. Here we explicitly discuss the range of validity of the approximations underlying our analytical model. We also show that the discrepancies pointed out for very small atom numbers and for very anisotropic traps are not surprising since these conditions exceed the range of validity of the model.