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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.
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Keywords:
- boundary effects /
- ideal Bose gas /
- Bose-Einstein condensation /
- harmonic potential
[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
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[12] Sisman A, Muller I 2004 Phys. Lett. A 320 360
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[16] Pang H, Dai W S, Xie M 2006 J. Phys. A: Math. Gen. 39 2563
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[20] Dai W S, Xie M 2004 Phys. Rev. E 70 016103
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[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
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[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 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 59 5271]
[57] [58] [59] Yuan D Q 2011 Acta Phys. Sin. 60 060509 (in Chinese)[袁都奇 2011 60 060509]
-
[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 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 59 5271]
[57] [58] [59] Yuan D Q 2011 Acta Phys. Sin. 60 060509 (in Chinese)[袁都奇 2011 60 060509]
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