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In the Thomas-Fermi semi-classical approximation, the maximal trap range and the real trap volume of ideal Fermi gas in an n-dimensional potential trap are gaven, and the relevant equations of state are derived. These results indicate that the maximal trap range and the real pressure of trapped gas are related to the potential field and the chemical potential of the free and ideal Fermi system. When the Thomas-Fermi approximate is valid and the condition ((kT)/(hω))2 ((16π2g)/(9N))2/3<<1 is satisfied, the application of the equation of state to three-dimensional spherical symmetry harmonic trap yields the result that the change of pressure is not obvious when the temperature changes, but the change of pressure is closely related to mass of particle, number of particles and the frequency of harmonic potential.
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Keywords:
- Fermi gas /
- n-dimensional potential trap /
- maximal trapped range /
- equation of state
[1] DeMarco B, Jin D S 1999 Science 285 1703
[2] Jochim S, Barterstein M, Altmeyer A, Hendl G, Riedl S, Chin C,Hecker Denschlag J, Grimm R 2003 Science 302 2101
[3] Greiner M, Regal C A, Jin D S 2003 Nature 426 537
[4] Modugno G, Roati G, Riboli F, Ferlaino F, Brecha R J, Inguscio M 2002 Science 297 2240
[5] Yin J P, Wang Z L 2005 Prog. Phys. 25 235 (in Chinese)[印建平、 王正岭 2005 物理学进展 25 235]
[6] Milstein J N, Kokkelmans S J J M F, Holland M J 2002 Phys. Rev. A 66 043604
[7] Ohashi Y, Griffin A 2003 Phys. Rev. A 67 063612
[8] Heiselberg H 2001 Phys. Rev. A 63 043606
[9] Ho T L 2004 Phys. Rev. Lett. 92 090402
[10] Falco G M, Stoof H T C 2004 Phys. Rev. Lett. 92 130401
[11] Perali A, Pieri P, Strinati G C 2004 Phys. Rev. Lett. 92 100404
[12] Kinnunen J, Rodriguez M, Torma P 2004 Science 305 1131
[13] Regal C A, Ticknor C, Bohn J L, Jin D S 2003 Nature 424 47
[14] Xiong H W, Liu S J, Zhang W P, Zhan M S 2005 Phys. Rev. Lett. 95 120401
[15] Stoof H T C, Houbiers M, Sackett C A, Hulet R G 1996 Phys. Rev. Lett. 76 10
[16] Yuan D Q 2006 Acta Phys. Sin. 55 3912 (in Chinese) (袁都 奇 2006 物理学报 55 3912)
[17] Men F D, Liu H 2006 Chin. Phys. 15 2856
[18] Men F D, Liu H, Zhu H Y 2008 Chin. Phys. B 17 3236
[19] Qin F, Chen J S 2009 Chin. Phys. B 18 2654
[20] Men F D, Liu H, Fan Z L, Zhu H Y 2009 Chin. Phys. B 18 2649
[21] Fan Z L, Men F D, Dou R B 2010 Acta Phys. Sin. 59 3715 (in Chinese) [范召兰、 门福殿、 窦瑞波 2010 物理学报 59 3715]
[22] Su G Z, Ou C J, Wang A Q P, Chen J C 2009 Chin. Phys. B 18 5189
[23] Huang Z F, Ou C J, Chen J C 2009 Chin. Phys. B 18 1380
[24] Butts D A, Rokhsar D S 1997 Phys. Rev. A 55 4346
[25] Chou T T, Yang C N, Yu I H 1997 Phys. Rev. A 55 4257
[26] Yan Z J 2000 Phys. Rev. A 61 063607
[27] Yan Z J, Chen L X, Chen J C, Chen C H 2001 J. Xiamen Univ. (Nat. Sci.) 40 220 (in Chinese)[严子浚、 陈丽璇、 陈金灿、 陈传鸿 2001 厦门大学学报 (自然科学版) 40 220]
[28] Yan Z J, Li M Z, Chen L X, Chen C H, Chen J C 1999 J. Phys. A 32 4069
[29] Pathria R K 1972 Statistical Mechanics (Oxford, New York, Toronto, Sydney, Braunschweig: Pergamon Press) p220
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[1] DeMarco B, Jin D S 1999 Science 285 1703
[2] Jochim S, Barterstein M, Altmeyer A, Hendl G, Riedl S, Chin C,Hecker Denschlag J, Grimm R 2003 Science 302 2101
[3] Greiner M, Regal C A, Jin D S 2003 Nature 426 537
[4] Modugno G, Roati G, Riboli F, Ferlaino F, Brecha R J, Inguscio M 2002 Science 297 2240
[5] Yin J P, Wang Z L 2005 Prog. Phys. 25 235 (in Chinese)[印建平、 王正岭 2005 物理学进展 25 235]
[6] Milstein J N, Kokkelmans S J J M F, Holland M J 2002 Phys. Rev. A 66 043604
[7] Ohashi Y, Griffin A 2003 Phys. Rev. A 67 063612
[8] Heiselberg H 2001 Phys. Rev. A 63 043606
[9] Ho T L 2004 Phys. Rev. Lett. 92 090402
[10] Falco G M, Stoof H T C 2004 Phys. Rev. Lett. 92 130401
[11] Perali A, Pieri P, Strinati G C 2004 Phys. Rev. Lett. 92 100404
[12] Kinnunen J, Rodriguez M, Torma P 2004 Science 305 1131
[13] Regal C A, Ticknor C, Bohn J L, Jin D S 2003 Nature 424 47
[14] Xiong H W, Liu S J, Zhang W P, Zhan M S 2005 Phys. Rev. Lett. 95 120401
[15] Stoof H T C, Houbiers M, Sackett C A, Hulet R G 1996 Phys. Rev. Lett. 76 10
[16] Yuan D Q 2006 Acta Phys. Sin. 55 3912 (in Chinese) (袁都 奇 2006 物理学报 55 3912)
[17] Men F D, Liu H 2006 Chin. Phys. 15 2856
[18] Men F D, Liu H, Zhu H Y 2008 Chin. Phys. B 17 3236
[19] Qin F, Chen J S 2009 Chin. Phys. B 18 2654
[20] Men F D, Liu H, Fan Z L, Zhu H Y 2009 Chin. Phys. B 18 2649
[21] Fan Z L, Men F D, Dou R B 2010 Acta Phys. Sin. 59 3715 (in Chinese) [范召兰、 门福殿、 窦瑞波 2010 物理学报 59 3715]
[22] Su G Z, Ou C J, Wang A Q P, Chen J C 2009 Chin. Phys. B 18 5189
[23] Huang Z F, Ou C J, Chen J C 2009 Chin. Phys. B 18 1380
[24] Butts D A, Rokhsar D S 1997 Phys. Rev. A 55 4346
[25] Chou T T, Yang C N, Yu I H 1997 Phys. Rev. A 55 4257
[26] Yan Z J 2000 Phys. Rev. A 61 063607
[27] Yan Z J, Chen L X, Chen J C, Chen C H 2001 J. Xiamen Univ. (Nat. Sci.) 40 220 (in Chinese)[严子浚、 陈丽璇、 陈金灿、 陈传鸿 2001 厦门大学学报 (自然科学版) 40 220]
[28] Yan Z J, Li M Z, Chen L X, Chen C H, Chen J C 1999 J. Phys. A 32 4069
[29] Pathria R K 1972 Statistical Mechanics (Oxford, New York, Toronto, Sydney, Braunschweig: Pergamon Press) p220
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