Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9612216 · Physical Review A

Energy of a trapped interacting Bose gas

Hualin Shi, Wei‐Mou Zheng

Published Oct 1, 1997• 17 citations
arXivHTMLPDF

Abstract

A Bose gas in an external potential is studied by means of the semiclassical approximation. Analytical results are derived for the energy of an interacting Bose gas in a generic power-law trapping potential. An expression for the chemical potential below the critical temperature is also obtained. The theoretical results are in agreement with a recent energy measurement.

DOI
10.1103/physreva.56.2984

Related papers

Critical temperature of a trapped interacting Bose-Einstein gas in the local-density approximation

Hualin Shi, Wei‐Mou Zheng

The Bose-Einstein gas in an external potential is studied by means of the local-density approximation. An analytical result is derived for the dependence of the critical temperature of Bose-Einstein condensation on the mutual interaction in a generic power-law potential.

arXiv:cond-mat/9609241•Physical Review A•Jul 1, 1997•38 citations

Chemical potential of a trapped interacting Bose gas

Zhuyue Zhang, Haixiang Fu, Jincan Chen +1 more

A Bose gas with repulsive interactions in a generic power-law potential is studied in the Hartree-Fock approximation. The scaling parameter characterizing the role of two-body repulsive interactions is expressed in terms of the scaled scattering length and the trap parameter. The chemical potential obtained here provides a correction to the existing analytical result, especially in the critical region of Bose-Einstein condensation.

Physical Review A•May 27, 2009•4 citations

Bose–Einstein condensation of a relativistic Bose gas trapped in a general external potential

Guozhen Su, Jincan Chen, Lixuan Chen

Bose–Einstein condensation of an ideal relativistic Bose gas trapped in a generic power-law potential is investigated. The analytical expressions for some important parameters such as the critical temperature, ground-state fraction and heat capacity are derived. The general criteria on the occurrence of Bose–Einstein condensation and the discontinuity of heat capacity at the critical temperature are obtained. The results obtained here present a unified description for the Bose–Einstein condensation of a class of ideal Bose systems so that many important conclusions in the literature are included in this paper.

Journal of Physics A Mathematical and General•Apr 19, 2006•12 citations

Bose-Einstein condensation in an external potential

Vanderlei Salvador Bagnato, David E. Pritchard, Daniel Kleppner

We present theoretical results for the critical temperature for Bose-Einstein condensation, condensate fraction, and heat capacity of a gas of Bose particles that are confined by a generic power-law potential trap. All three of these quantities are found to vary markedly with the shape of the potential. Both the ideal and the weakly interacting Bose gas are considered.

Physical Review A•May 1, 1987•435 citations

An analytical description of the low temperature behaviour of a weakly interacting Bose gas

Guozhen Su, Lixuan Chen, Jincan Chen

An analytical description of the low temperature behaviour of a trapped interacting Bose gas is presented by using a simple approach that is based on the principle of the constancy of chemical potentials in equilibrium and the local-density approximation. Several thermodynamic quantities, which include the ground-state fraction, chemical potential, total energy, entropy and heat capacity, are derived analytically. It is shown that the results obtained here are in excellent agreement with the experimental data and the theoretical predictions based on the numerical calculation. Meanwhile, by selecting a suitable variable, the divergent problem existing in some papers is solved.

Journal of Physics A Mathematical and General•Feb 11, 2004•4 citations

CRITICAL TEMPERATURE OF AN INTERACTING BOSE GAS IN A GENERIC POWER-LAW POTENTIAL

Luca Salasnich

We investigate the critical temperature of an interacting Bose gas confined in a trap described by a generic isotropic power-law potential. We compare the results with respect to the non-interacting case. In particular, we derive an analytical formula for the shift of the critical temperature holding to first order in the scattering length. We show that this shift scales as Nn/3(n+2), where N is the number of Bosons and n is the exponent of the power-law potential. Moreover, the sign of the shift critically depends on the power-law exponent n. Finally, we find that the shift of the critical temperature due to finite-size effects vanishes as N-2n/3(n+2).

arXiv:cond-mat/0204402•International Journal of Modern Physics B•Jun 30, 2002•11 citations
A Bose gas in an external potential is studied by means of the semiclassical approximation. Analytical results are derived for the energy of an interacting Bose gas in a generic power-law trapping potential. An expression for the chemical potential below the critical temperature is also obtained. The theoretical results are in agreement with a recent energy measurement.
Bose–Einstein condensation of an ideal relativistic Bose gas trapped in a generic power-law potential is investigated. The analytical expressions for some important parameters such as the critical temperature, ground-state fraction and heat capacity are derived. The general criteria on the occurrence of Bose–Einstein condensation and the discontinuity of heat capacity at the critical temperature are obtained. The results obtained here present a unified description for the Bose–Einstein condensation of a class of ideal Bose systems so that many important conclusions in the literature are included in this paper.
An analytical description of the low temperature behaviour of a trapped interacting Bose gas is presented by using a simple approach that is based on the principle of the constancy of chemical potentials in equilibrium and the local-density approximation. Several thermodynamic quantities, which include the ground-state fraction, chemical potential, total energy, entropy and heat capacity, are derived analytically. It is shown that the results obtained here are in excellent agreement with the experimental data and the theoretical predictions based on the numerical calculation. Meanwhile, by selecting a suitable variable, the divergent problem existing in some papers is solved.
We investigate the critical temperature of an interacting Bose gas confined in a trap described by a generic isotropic power-law potential. We compare the results with respect to the non-interacting case. In particular, we derive an analytical formula for the shift of the critical temperature holding to first order in the scattering length. We show that this shift scales as Nn/3(n+2), where N is the number of Bosons and n is the exponent of the power-law potential. Moreover, the sign of the shift critically depends on the power-law exponent n. Finally, we find that the shift of the critical temperature due to finite-size effects vanishes as N-2n/3(n+2).