Thermodynamic properties of a finite Bose gas in a harmonic trap

doi:10.1088/1674-1056/19/5/050502

中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50502-050502.doi: 10.1088/1674-1056/19/5/050502

Thermodynamic properties of a finite Bose gas in a harmonic trap

王建辉, 马永利

Department of Physics, Fudan University, Shanghai 200433, China

收稿日期:2009-09-18 修回日期:2009-09-30 出版日期:2010-05-15 发布日期:2010-05-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10775032 and 10574028).

Thermodynamic properties of a finite Bose gas in a harmonic trap

Wang Jian-Hui(王建辉) and Ma Yong-Li(马永利)^†

Department of Physics, Fudan University, Shanghai 200433, China

Received:2009-09-18 Revised:2009-09-30 Online:2010-05-15 Published:2010-05-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10775032 and 10574028).

摘要/Abstract

摘要： We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of total number $N$ of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, specially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.

Abstract: We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of total number N of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, specially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.

Key words: trapped finite bosons, simple explicit distribution law, thermodynamics, finite-size scaling

中图分类号: (Boson systems)

05.30.Jp

03.75.Hh (Static properties of condensates; thermodynamical, statistical, and structural properties) 05.30.Ch (Quantum ensemble theory) 05.70.Ce (Thermodynamic functions and equations of state)

王建辉, 马永利. Thermodynamic properties of a finite Bose gas in a harmonic trap[J]. 中国物理B, 2010, 19(5): 50502-050502.

Wang Jian-Hui(王建辉) and Ma Yong-Li(马永利). Thermodynamic properties of a finite Bose gas in a harmonic trap[J]. Chin. Phys. B, 2010, 19(5): 50502-050502.

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Thermodynamic properties of a finite Bose gas in a harmonic trap

Thermodynamic properties of a finite Bose gas in a harmonic trap

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