囚禁有限unitary费米气体的热力学性质

袁都奇

doi:10.7498/aps.65.180302

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摘要

应用分数不相容统计，研究了三维简谐势阱中有限unitary费米气体在绝对零度和有限温度下的热力学性质，并与势阱中满足热力学极限条件的unitary费米气体进行了比较. 结果表明：绝对零度时有限系统的费米能、粒子平均能量随粒子数的增加而增大，并以满足热力学极限系统的对应物理量为上限，有限系统的费米能、粒子平均能量随势阱边界变化存在极大值. 有限温度条件下给定粒子数时，有限系统的粒子平均能量、粒子平均熵、粒子平均热容量分别存在对应的特征温度，当温度等于物理量对应的特征温度时，有限系统与满足热力学极限系统的同一物理量相等，低于（或高于）物理量对应的特征温度时，有限系统的物理量将大于（或小于）满足热力学极限系统的同一量. 给定温度条件下，有限系统粒子平均能量、粒子平均熵、粒子平均热容量分别存在对应的特征粒子数，当粒子数等于物理量对应的特征粒子数时，有限系统与满足热力学极限系统的同一物理量相等，少于（或多于）物理量对应的特征粒子数时，有限系统的物理量将小于（或大于）满足热力学极限系统的同一量.

关键词:

作者及机构信息

袁都奇

1.
宝鸡文理学院物理与光电技术学院, 宝鸡 721016

通信作者: 袁都奇, yuanduqi@163.com

基金项目: 陕西省自然科学基金（批准号：2012JM1006）资助的课题.

参考文献

[1]	Regal C A, Greiner M, Jin D S 2004 Phys. Rev. Lett. 92 040403
[2]	Bourdel T, Khaykovich L, Cubizolles J, Zhang J, Chevy F, Teichmann M, Tarruell L, Kokkelmans S J J M F, Salomon C 2004 Phys. Rev. Lett. 93 050401
[3]	Bartenstein M, Altmeyer A, Riedl S, Jochim S, Chin C, Denschlag H J, Grimm R 2004 Phys. Rev. Lett. 92 120401
[4]	Zwierlein M W, Abo-Shaeer J R, Schirotzek A, Schunck C H, Ketterle W 2005 Nature 435 1047
[5]	Romans M W J, Stoof H T C 2005 Phys. Rev. Lett. 95 260407
[6]	Ho T L 2004 Phys. Rev. Lett. 92 090402
[7]	Hu H, Drummond P D, Liu X J 2007 Nat. Phys. 3 469
[8]	Luo L, Clancy B, Joseph J, Kinast J, Thomas J E 2007 Phys. Rev. Lett. 98 080402
[9]	Kinast J, Turlapov A, Thomas J E, Chen Q J, Stajic J, Levin K 2005 Science 307 1296
[10]	Luo L, Thomas J E 2009 J. Low Temp. Phys. 154 1
[11]	Joseph J, Clancy B, Luo L, Kinast J, Turlapov A, Thomas J E 2007 Phys. Rev. Lett. 98 170401
[12]	Papenbrock T 2005 Phys. Rev. A 72 041603
[13]	Hu H, Liu X J, Drummond P D 2010 New J. Phys. 12 063038
[14]	Bulgac A, Drut J E, Magierski P 2006 Phys. Rev. Lett. 96 090404
[15]	Haldane F D M 1991 Phys. Rev. Lett. 67 937
[16]	Wu Y S 1994 Phys. Rev. Lett. 73 922
[17]	Bhaduri R K, Murthy M V N, Srivastava M K 2007 J. Phys. B: At. Mol. Opt. Phys. 40 1775
[18]	Qin F, Chen J S 2009 Phys. Rev. A 79 043625
[19]	Bhaduri R K, Murthy M V N, Brack M 2008 J. Phys. B : At. Mol. Opt. Phys. 41 115301
[20]	Qin F, Chen J S 2010 J. Phys. B: At. Mol. Opt. Phys. 43 055302
[21]	Qin F, Chen J S 2012 Phys. Lett. A 376 1191
[22]	Liu K, Chen J S 2011 Chin. Phys. B 20 020501
[23]	Sevinli S, Tanatar B 2007 Phys. Lett. A 371 389
[24]	Franco D, Stefano G, Lev P P, Sandro S 1999 Rev. Mod.Phys. 71 463
[25]	Sisman A, Muller I 2004 Phys. Lett. A 320 360
[26]	Sisman A 2004 J. Phys. A: Math. Gen. 37 11353
[27]	Pang H, Dai W S, Xie M 2006 J. Phys. A: Math. Gen. 39 2563
[28]	Dai W S, Xie M 2003 Phys. Lett. A 311 340
[29]	Su D G, Ou C J, Wang A Q P, Chen J C 2009 Chin. Phys. B 18 5189
[30]	Yuan D Q 2014 Acta Phys. Sin. 63 170501 (in Chinese) [袁都奇 2014 物理学报 63 170501]
[31]	Iguchi K 1997 Phys. Rev. Lett. 78 3233
[32]	Hassan A S, EI-Badry A M 2009 Physica B 404 1947
[33]	Ingold G L, Lambrecht A A 1998 Eur. Phys. J. D 1 29

施引文献

[1]	Regal C A, Greiner M, Jin D S 2004 Phys. Rev. Lett. 92 040403
[2]	Bourdel T, Khaykovich L, Cubizolles J, Zhang J, Chevy F, Teichmann M, Tarruell L, Kokkelmans S J J M F, Salomon C 2004 Phys. Rev. Lett. 93 050401
[3]	Bartenstein M, Altmeyer A, Riedl S, Jochim S, Chin C, Denschlag H J, Grimm R 2004 Phys. Rev. Lett. 92 120401
[4]	Zwierlein M W, Abo-Shaeer J R, Schirotzek A, Schunck C H, Ketterle W 2005 Nature 435 1047
[5]	Romans M W J, Stoof H T C 2005 Phys. Rev. Lett. 95 260407
[6]	Ho T L 2004 Phys. Rev. Lett. 92 090402
[7]	Hu H, Drummond P D, Liu X J 2007 Nat. Phys. 3 469
[8]	Luo L, Clancy B, Joseph J, Kinast J, Thomas J E 2007 Phys. Rev. Lett. 98 080402
[9]	Kinast J, Turlapov A, Thomas J E, Chen Q J, Stajic J, Levin K 2005 Science 307 1296
[10]	Luo L, Thomas J E 2009 J. Low Temp. Phys. 154 1
[11]	Joseph J, Clancy B, Luo L, Kinast J, Turlapov A, Thomas J E 2007 Phys. Rev. Lett. 98 170401
[12]	Papenbrock T 2005 Phys. Rev. A 72 041603
[13]	Hu H, Liu X J, Drummond P D 2010 New J. Phys. 12 063038
[14]	Bulgac A, Drut J E, Magierski P 2006 Phys. Rev. Lett. 96 090404
[15]	Haldane F D M 1991 Phys. Rev. Lett. 67 937
[16]	Wu Y S 1994 Phys. Rev. Lett. 73 922
[17]	Bhaduri R K, Murthy M V N, Srivastava M K 2007 J. Phys. B: At. Mol. Opt. Phys. 40 1775
[18]	Qin F, Chen J S 2009 Phys. Rev. A 79 043625
[19]	Bhaduri R K, Murthy M V N, Brack M 2008 J. Phys. B : At. Mol. Opt. Phys. 41 115301
[20]	Qin F, Chen J S 2010 J. Phys. B: At. Mol. Opt. Phys. 43 055302
[21]	Qin F, Chen J S 2012 Phys. Lett. A 376 1191
[22]	Liu K, Chen J S 2011 Chin. Phys. B 20 020501
[23]	Sevinli S, Tanatar B 2007 Phys. Lett. A 371 389
[24]	Franco D, Stefano G, Lev P P, Sandro S 1999 Rev. Mod.Phys. 71 463
[25]	Sisman A, Muller I 2004 Phys. Lett. A 320 360
[26]	Sisman A 2004 J. Phys. A: Math. Gen. 37 11353
[27]	Pang H, Dai W S, Xie M 2006 J. Phys. A: Math. Gen. 39 2563
[28]	Dai W S, Xie M 2003 Phys. Lett. A 311 340
[29]	Su D G, Ou C J, Wang A Q P, Chen J C 2009 Chin. Phys. B 18 5189
[30]	Yuan D Q 2014 Acta Phys. Sin. 63 170501 (in Chinese) [袁都奇 2014 物理学报 63 170501]
[31]	Iguchi K 1997 Phys. Rev. Lett. 78 3233
[32]	Hassan A S, EI-Badry A M 2009 Physica B 404 1947
[33]	Ingold G L, Lambrecht A A 1998 Eur. Phys. J. D 1 29

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囚禁有限unitary费米气体的热力学性质

1. 宝鸡文理学院物理与光电技术学院, 宝鸡 721016

通信作者: 袁都奇, yuanduqi@163.com

基金项目:

陕西省自然科学基金（批准号：2012JM1006）资助的课题.

收稿日期: 2016-05-19

修回日期: 2016-06-13

刊出日期: 2016-09-05

摘要: 应用分数不相容统计，研究了三维简谐势阱中有限unitary费米气体在绝对零度和有限温度下的热力学性质，并与势阱中满足热力学极限条件的unitary费米气体进行了比较. 结果表明：绝对零度时有限系统的费米能、粒子平均能量随粒子数的增加而增大，并以满足热力学极限系统的对应物理量为上限，有限系统的费米能、粒子平均能量随势阱边界变化存在极大值. 有限温度条件下给定粒子数时，有限系统的粒子平均能量、粒子平均熵、粒子平均热容量分别存在对应的特征温度，当温度等于物理量对应的特征温度时，有限系统与满足热力学极限系统的同一物理量相等，低于（或高于）物理量对应的特征温度时，有限系统的物理量将大于（或小于）满足热力学极限系统的同一量. 给定温度条件下，有限系统粒子平均能量、粒子平均熵、粒子平均热容量分别存在对应的特征粒子数，当粒子数等于物理量对应的特征粒子数时，有限系统与满足热力学极限系统的同一物理量相等，少于（或多于）物理量对应的特征粒子数时，有限系统的物理量将小于（或大于）满足热力学极限系统的同一量.

关键词:

Thermodynamics of trapped finite unitary Fermi gas

1.
College of Physics and Photoelectric Technology, Baoji University of Science and Arts, Baoji 721016, China

Fund Project:

Project supported by the Natural Science Foundation of Shaanxi Province, China (Grant No. 2012JM1006).

Received Date: 19 May 2016

Accepted Date: 13 June 2016

Published Online: 05 September 2016

Abstract: At zero-temperature and finite-temperature, the thermodynamic properties of finite unitary Fermi gas in a three-dimensional harmonic trap are investigated by using fractional exclusion statistics, and the results are compared with those of the system which satisfies the thermodynamic limit. At zero-temperature, Fermi energy and average energy of per particle increase with the increase of the number of particles for finite unitary Fermi gas, and their limits are the corresponding parameters of the system which satisfy thermodynamic limits. Fermi energy and average energy of per particle each have a maximum value changing with the boundary of the potential well. For the finite-temperature trapped unitary Fermi system, when the number of particles is certain the average energy of per particle, average entropy of per particle, average heat capacity of per particle each have a characteristic temperature, respectively, when the temperature is equal to the characteristic temperature of the physical parameter, the corresponding parameters for the finite system and the thermodynamic limit system are equal, when the temperature is lower (or higher) than the characteristic temperature of parameter, the physical parameter of the finite system will be greater (or less) than the corresponding parameter of the thermodynamic limit system. The characteristic temperature has particle number effect and boundary effect. When the temperature is determined, the average energy of per particle, average entropy of per particle and average heat capacity of per particle each have a characteristic number of particles, respectively, when the number of particles is equal to the characteristic number of particles for physical parameter, the corresponding parameters for the finite system and the thermodynamic limit system are equal, when the number of particles is less (or more) than the characteristic number of particles for corresponding parameter, the corresponding parameter of the finite system will be less (or larger) than the thermodynamic limit of system.

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