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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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Keywords:
- finite unitary Fermi gas /
- harmonic potential /
- particles number effects /
- boundary effects
[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 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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[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 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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