Abstract
Thermodynamic quantities, occupation numbers and their fluctuations of a one-dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in microcanonical ensemble. The visible difference of the ground state occupation number in grand-canonical ensemble and microcanonical ensemble is found to decrease by power law as the number of particles increases.
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M H Anderson, J R Ensher, M R Matthews, C E Wieman and E A Cornell, Science 269, 198 (1995)
K B Davis, M O Mewes, M R Andrews, N J van Druten, D S Durfee, D M Kurn and W Ketterle, Phys. Rev. Lett. 75, 3969 (1995)
C C Bradley, C A Sackett, J J Tollett and R G Hulet, Phys. Rev. Lett. 75, 1687 (1995)
E Timmermans, P Tommasini, M Hussein and A Kerman, Phys. Rep. 315, 199 (1999)
R A Duine and H T C Stoof, Phys. Rep. 396, 115 (2004)
J Gemmer, M Michel and G Mahler, Quantum thermodynamics (Springer, Berlin, 2004)
T D Kieu, Phys. Rev. Lett. 93, 140403 (2006)
J Klaers, J Schmitt, F Vewinger and M Weitz, Nature 468, 545 (2010)
J Schmitt, T Damm, D Dung, F Vewinger, J Klaers and M Weitz, Phys. Rev. Lett. 112, 030401 (2014)
J X Hou, X Wang, S Huang, J J Lin, C L Wang and Q H Liu, Acta Phys. Sin. 55, 1616 (2006)
T C P Chui, D R Swanson, M J Adriaans, J A Nissen and J A Lipa, Phys. Rev. Lett. 69, 3005 (1992)
S Grossmann and M Holthaus, Phys. Rev. E 54, 3495 (1996)
M Holthaus, E Kalinowski and K Kirsten, Ann. Phys. 270, 198 (1998)
V Bagnato and D Kleppner, Phys. Rev. A 44, 7439 (1991)
W Ketterle and N J van Druten, Phys. Rev. A 54, 656 (1996)
C Herzog and M Olshanii, Phys. Rev. A 55, 3254 (1997)
J Catani, G Barontini, G Lamporesi, F Rabatti, G Thalhammer, F Minardi, S Stringari and M Ingusci, Phys. Rev. Lett. 103, 140401 (2009)
J X Hou, Phys. Lett. A 368, 366 (2007)
G Q Li, L B Fu, J K Xue, X Z Chen and J Liu, Phys. Rev. A 74, 055601 (2006)
J X Hou, J. Low Temp. Phys. 177, 305 (2014)
R K Pathria, Statistical mechanics (Butterworth-Heinemann, Singapore, 1996)
G E Andrews, The theory of partitions (Addison-Wesley, Reading, 1976)
H Rademacher, Proc. Natl Acad. Sci. 23, 78 (1937)
G H Hardy and S Ramanujan, Proc. London Math. Soc. 17, 75 (1918)
P Erdos and J Lehner, Duke Math. J. 8, 335 (1941)
F C Auluck, S Chowla and H Gupta, J. Ind. Math. Soc. 6, 105 (1942)
Acknowledgements
This work was jointly supported by the National Natural Science Foundation of China under Grant No. 11304037, the Natural Science Foundation of Jiangsu Province, China under Grant BK20130604, the Ph.D. Programs Foundation of Ministry of Education of China under Grant No. 20130092120041, the Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China under Grant No. 7907020002.
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HOU, JX., YANG, J. Bose gases in one-dimensional harmonic trap. Pramana - J Phys 87, 60 (2016). https://doi.org/10.1007/s12043-016-1262-2
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DOI: https://doi.org/10.1007/s12043-016-1262-2