Thermodynamic properties of a finite Bose gas in a harmonic trap

• Published in: Chinese physics B Vol. 19; no. 5; pp. 78 - 84
• Main Author: 王建辉 马永利
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.05.2010
• Subjects: Approximation; Condensates; Harmonics; Mathematical analysis; Occupation; Temperature dependence; Thermodynamic properties; Transition temperature; 有限尺寸; 温度依赖性; 热力学性质; 热力学行为; 玻色系统; 理想玻色气体; 调和势
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/19/5/050502

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 the 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, especially 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.