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

Acta Sinica Quantum Optica

Bose-Einstein Condensation in External Potential

Guofeng Zhang

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

In this paper, (1) a kind of meaning of the BEC concept and the condition of the BEC formation of synopsis are introduced.(2) we demonstrate the possibility of BEC of an ideal Bose gas confined by one-and two-dimensional power-law traps. One-dimensional systems display BEC in traps that are more confined than parabolic: U(x)~xη, η2, Two-dimensional systems display BEC for any finite Value of η.

Related papers

Bose-Einstein condensation in low-dimensional traps

Vanderlei Salvador Bagnato, Daniel Kleppner

We demonstrate the possibility of Bose-Einstein condensation (BEC) of an ideal Bose gas confined by one- and two-dimensional power-law traps. One-dimensional systems display BEC in traps that are more confining than parabolic: U(x)\ensuremath{\sim}${\mathit{x}}^{\mathrm{\ensuremath{\eta}}}$,\ensuremath{\eta}2. Two-dimensional systems display BEC for any finite value of \ensuremath{\eta}. A possible experimental configuration for a two-dimensional trap is described.

Physical Review A•Dec 1, 1991•385 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

Bose-Einstein condensation of a trapped gas in n dimensions

Zijun Yan

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.

Physical Review A•Jun 1, 1999•29 citations

BEC IN NONEXTENSIVE STATISTICAL MECHANICS: SOME ADDITIONAL RESULTS

LUCA SALASNICH

In a recent paper1 we discussed the Bose–Einstein condensation (BEC) in the framework of Tsallis's nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction.

arXiv:cond-mat/0101350•International Journal of Modern Physics B•Apr 10, 2001•7 citations

Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions

Wolfgang Ketterle, N. J. van Druten

Bose-Einstein condensation (BEC) of an ideal gas is investigated for a finite number of particles. In three dimensions, we find a transition temperature which is lower than in the thermodynamic limit. Lowering the dimension increases the transition temperature and is therefore favorable for BEC. This is in contrast to the standard result obtained in the thermodynamic limit which states that BEC is not possible in, e.g., a one-dimensional (1D) harmonic potential. As a result, 1D atom traps, such as radially tightly confining magnetic traps or optical dipole traps, are promising for studying BEC. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Jul 1, 1996•520 citations

BEC in Nonextensive Statistical Mechanics: Some Additional Results

Luca Salasnich

In a recent paper [Int. J. Mod. Phys. B 14, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis’s nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction. PACS numbers: 05.30-d; 03.75.Fi 1 Recently we analyzed the consequences of weak nonextensivity on Bose-Einstein Condensation for an ideal Bose gas 1 by using Tsallis’s nonextensive statistical mechanics (NSM). 2 From the nonextensive Bose-Einstein distribution 3−5 we derived the BEC transition temperature, the condensed fraction and the energy per particle in three different cases: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. In this short contribution we generalize our previous results by considering the ideal Bose gas in a generic power-law potential. All the calculations are performed by assuming a D-dimensional space. The NSM predicts that, for an ideal quantum gas of identical bosons in the grand canonical ensemble, the weak nonextensivity formula of the average number of particles with energy ǫ is given by 〈n(ǫ)〉q = 1

•Jan 1, 2001•7 citations
In this paper, (1) a kind of meaning of the BEC concept and the condition of the BEC formation of synopsis are introduced.(2) we demonstrate the possibility of BEC of an ideal Bose gas confined by one-and two-dimensional power-law traps. One-dimensional systems display BEC in traps that are more confined than parabolic: U(x)~xη, η2, Two-dimensional systems display BEC for any finite Value of η.
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.
Bose-Einstein condensation (BEC) of an ideal gas is investigated for a finite number of particles. In three dimensions, we find a transition temperature which is lower than in the thermodynamic limit. Lowering the dimension increases the transition temperature and is therefore favorable for BEC. This is in contrast to the standard result obtained in the thermodynamic limit which states that BEC is not possible in, e.g., a one-dimensional (1D) harmonic potential. As a result, 1D atom traps, such as radially tightly confining magnetic traps or optical dipole traps, are promising for studying BEC. \textcopyright{} 1996 The American Physical Society.
In a recent paper [Int. J. Mod. Phys. B 14, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis’s nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction. PACS numbers: 05.30-d; 03.75.Fi 1 Recently we analyzed the consequences of weak nonextensivity on Bose-Einstein Condensation for an ideal Bose gas 1 by using Tsallis’s nonextensive statistical mechanics (NSM). 2 From the nonextensive Bose-Einstein distribution 3−5 we derived the BEC transition temperature, the condensed fraction and the energy per particle in three different cases: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. In this short contribution we generalize our previous results by considering the ideal Bose gas in a generic power-law potential. All the calculations are performed by assuming a D-dimensional space. The NSM predicts that, for an ideal quantum gas of identical bosons in the grand canonical ensemble, the weak nonextensivity formula of the average number of particles with energy ǫ is given by 〈n(ǫ)〉q = 1