三维简谐势阱中玻色-爱因斯坦凝聚的边界效应

袁都奇

doi:10.7498/aps.63.170501

摘要

在定义特征长度的基础上，应用Euler-MacLaurin公式，研究了理想玻色气体在三维简谐势阱中玻色-爱因斯坦凝聚的边界效应. 结果表明：粒子的凝聚分数由于有限尺度和有限粒子数效应而减小，修正的凝聚分数和凝聚温度由于边界效应存在一个极大值，选择优化的最佳势阱参数，可以有效提高凝聚分数和凝聚温度；热容量的跃变存在边界效应和粒子数效应，选择合理的势阱参数时，热容量的跃变存在一个极小值. 导出了简谐势阱中有限理想玻色气体的状态方程，揭示了压强的各向异性（或各向同性）取决于简谐势频率的各向异性（或各向同性）.

关键词:

Abstract

By defining the characteristic length, the boundary effects of Bose-Einstein condensation in a three-dimensional harmonic trap are investigated using the Euler-MacLaurin formula. Results show that the condensed fraction of particles reduces due to the finite-size effects and the effects of finite particle number; the corrections of the condensation fraction and the condensation temperature have, respectively, a maximum value due to the boundary effect, hence it is very effective to optimize the parameters of the harmonic traps for improving the condensation fraction and the condensation temperature. In the jump of heat capacity exist the boundary effects and the effects of finite particle number, and the jump of heat capacity has a minimum because the parameters of harmonic traps are selected to be reasonable. The equation of state is derived for a finite ideal Bose gas system in a three-dimensional harmonic trap; the anisotropy (or isotropy) of the pressure is determined by the anisotropy (or isotropy) of the frequency of the harmonic potential.

Keywords:

作者及机构信息

袁都奇

1.
宝鸡文理学院物理与信息技术系, 宝鸡 721016

基金项目: 陕西省自然科学计划项目（批准号：2012JM1006）和宝鸡文理学院重点科研项目（批准号：ZK11045）资助的课题.

Authors and contacts

Yuan Du-Qi

1.
Department of Physics and Information Technology, Baoji University of Science and Arts, Baoji 721016, China

Funds: Project supported by the Natural Science Foundation of the Shaanxi Province, China (Grant No. 2012JM1006), and the key project of Baoji University of Sciences and Arts of China (Grant No. ZK11045).

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施引文献

[1]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[2]
[3]	Bagnato V, Pritchard D E, Kleppner D 1987 Phys. Rev. A 35 4354
[4]
[5]	Grossmann S, Holthaus M 1995 Phys. Lett A 208 188
[6]	Ensher J R, Jin D S, Matthews M R, Wieman C E, Cornell E A 1996 Phys. Rev. Lett 77 4984
[7]
[8]	Haugerud H, Haugset T, Ravndal F 1997 Phys. Leet. A 225 18
[9]
[10]
[11]	Yan Z 2000 Phys. Rev. A 61 063607
[12]	Sisman A, Muller I 2004 Phys. Lett. A 320 360
[13]
[14]
[15]	Sisman A 2004 J. Phys. A: Math. Gen. 37 11353
[16]	Pang H, Dai W S, Xie M 2006 J. Phys. A: Math. Gen. 39 2563
[17]
[18]
[19]	Dai W S, Xie M 2003 Phys. Lett. A 311 340
[20]	Dai W S, Xie M 2004 Phys. Rev. E 70 016103
[21]
[22]	Begun V V, Gorenstein M I 2008 Phys. Rev. C 77 064903
[23]
[24]
[25]	Nash C, O'Connor D 1999 Ann. Phys. 273 72
[26]
[27]	Leboeuf P, Monastra A G 2002 Ann. Phys. 297 127
[28]	Chamati H 2008 J. Phys. A: Math. Theor. 41 375002
[29]
[30]
[31]	Sun J R, Wei Y N, Pu F C 1995 Acta Phys. Sin. 4 542
[32]
[33]	Wu S Q, Wang S J, Sun W L, Yu W L 2004 Chin. Phys. 13 510
[34]
[35]	Su D G, Ou C J, Wang A Q P, Chen J C 2009 Chin. Phys B 18 5189
[36]	Hassan A S 2010 Phys. Lett. A 374 2106
[37]
[38]
[39]	Hassan A S, EI-Badry A M, Mohammedein A M, Ebeid M R 2012 Phys. Lett. A 376 1781
[40]
[41]	Cui H T, Wang L C, Yi X X 2004 Acta Phys. Sin. 53 991 (in Chinese)[崔海涛, 王成林, 衣学喜 2004 物理学报 53 991]
[42]
[43]	Ketterle W, Druten N J V 1996 Phys. Rev. A 54 656
[44]
[45]	Pathria R K 1998 Phys. Rev. A 58 1490
[46]
[47]	Franco D, Stefano G, Lev P P, Sandro S 1999 Rev. Mod. Phys. 71 463
[48]	Pathria R K 1972 Statistical Mechanics (Oxford: Pergamon) p177
[49]
[50]	Yan Z J, Li M Z, Chen L X, Chen C H, Chen J C 1999 J. Phys. A: Math. Gen. 32 4069
[51]
[52]
[53]	Gerbier F, Thywissen J H, Richard S, Hugbart M, Bouyer P, Aspecr A 2004 Phys. Rev. A 70 013607
[54]
[55]	Hassan A S, EI-Badry A M 2009 Physica B 404 1947
[56]	Yuan D Q 2010 Acta Phys. Sin. 59 5271 (in Chinese)[袁都奇 2010 物理学报 59 5271]
[57]
[58]
[59]	Yuan D Q 2011 Acta Phys. Sin. 60 060509 (in Chinese)[袁都奇 2011 物理学报 60 060509]

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