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在考虑到广义不确定性原理时, 统计物理中的态密度必须做出修正, 这导致对传统统计物理的所有结果都有不同程度的修正. 在高能、高温条件下, 此修正是颠覆传统观念的, 在低温条件下, 也有一定的修正. 研究了低温条件下考虑到广义不确定性原理时, 理想费米气体和具有弱相互作用费米气体的热力学性质, 分别给出理想费米气体和弱相互作用费米气体的化学势、内能和定容热容的解析表达式, 并以铜电子气体为例进行了具体数值计算, 将计算结果与不考虑广义不确定性原理时的费米气体的热力学性质进行了比较, 探讨了广义不确定性原理对系统热力学性质的影响. 考虑到广义不确定性原理后费米气体的化学势、费米能和基态能增大, 热容减少, 内能随温度的增加先增大, 到某一温度(对于铜电子气体, T/TF0～0.3)时, 增值为零, 温度再增加内能减少. 这些修正的具体数值主要由粒子数密度决定, 粒子数密度越大, 修正越大.When taking into account the generalized uncertainty principle in statistical physics, the density of states must make a correction, which causes all the results of traditional statistical physics to have different degrees of correction. In high-energy or high-temperature conditions, this amendment can subvert the traditional concept and there are also some certain amendments at low temperatures. In this paper we study the thermodynamic properties of the ideal and weakly interacting Fermi gas in low temperature conditions when the generalized uncertainty principle is taken into account. Firstly, analytical expressions of chemical potential, internal energy and heat capacity at constant volume of ideal or weakly interacting Fermi gas are given. Then the properties of copper electron gas are computed as an example, showing that when the generalized uncertainty principle is taken into account the chemical potential, Fermi energy and the ground state energy increase with the increase of temperature, while the heat capacity decreases. When the temperature is lower than 0.3 times TF0, the internal energy increases with the increase of temperature, but becomes decreased when temperature is high than 0.3 times TF0. These amendments are mostly dependent on particle density, which becomes bigger and bigger with particle density increasing.
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Keywords:
- generalized uncertainty principle /
- Fermi gas /
- thermodynamic property
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[34] Dehmelt H 1988 Phys. Scr. T22 102
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[1] Townsend P K 1977 Phys. Rev. D 15 2795
[2] Gross D J, Mende P F 1988 Nucl. Phys. B 303 407
[3] Amati D, Ciafaloni M, Veneziano G 1989 Phys. Lett. B 216 41
[4] Konishi K, Pauffti G, Provero P 1990 Phys. Lett. B 234 276
[5] Jaeckel M J, Reynaud S 1994 Phys. Lett. A 185 143
[6] Garay L 1995 Int. J. Mod. Phys. A 10 145
[7] Kempf A, Mangano G, Mann R B 1995 Phys. Rev. D 52 1108
[8] Kempf A, Mangano G 1997 Phys. Rev. D 55 7909
[9] Nozari K, Etemadi A 2012 Phys. Rev. D 85 104029
[10] Ghosh S Roy P 2012 Phys. Lett. B 711 423
[11] Chang L N, Minic D, Takeuchi T, Okamura N 2002 Phys. Rev. D 65 125028
[12] Li X 2002 Phys. Lett. B 540 9
[13] Fityo V T 2008 Phys. Lett. A 372 5872
[14] Chang L N, Minic D, Okamura N, Takeuchi T 2002 Phys. Rev. D 65 125027
[15] Vakili B, Gorji M A 2012 J. Stat. Mech. p10013
[16] Jochim S, Bartenstein M, Altmeyer A, Hendl G, Riedl S, Chin C, Hecker Denschlag J, Grimm R 2003 Science 302 2101
[17] Kinast J, Hemmer S L, Gehm M E, Turlapov A, Thomas J E 2004 Phys. Rev. Lett. 92 150402
[18] Bartenstein M, Altmeyer A, Riedl S, Jochim S, Chin C, Denschlag J H, Grimm R 2004 Phys. Rev. Lett. 92 203201
[19] Kinast J, Turlapov A, Thomas J E, Chen Q J, Stajic J, Levin K 2005 Science 307 1296
[20] Zwierlein M W, Abo-Shaeer J R, Schirotzek A, Schunck C H, Ketterle W 2005 Nature 435 1047
[21] Xiong H W, Liu S J, Zhang W P, Zhan M S 2005 Phys. Rev. Lett. 95 120401
[22] Su G Z, Chen L X 2004 Acta Phys. Sin. 53 984 (in Chinese) [苏国珍, 陈丽璇 2004 53 984]
[23] Men F D, Fan Z L 2010 Chin. Phys. B 19 030502
[24] Dong H, Ma Y L 2009 Chin. Phys. B 18 0715
[25] Zhao R, Zhang L C, Li H F 2009 Acta Phys. Sin. 58 2193 (in Chinese) [赵仁, 张丽春, 李怀繁 2009 58 2193]
[26] Quesne C, Tkachuk V M 2004 J. Phys. A: Math. General 37 10095
[27] Brau F 1999 J. Phys. A: Math. General 32 7691
[28] Benczik S, Chang L N, Minic D, Takeuchi T 2005 Phys. Rev. A 72 012104
[29] Stetsko M M, Tkachuk V M 2006 Phys. Rev. A 74 012101
[30] Brau F, Buisseret F 2006 Phys. Rev. D 74 036002
[31] Pathria R K 1977 Statistical Mechanics (London: Pergamon Press)
[32] Huang K 1987 Statistical Mechanics (New York: Wiley) p272
[33] Li H L, Wang J J, Yang B, Shen H J 2015 Acta Phys. Sin. 64 040501 (in Chinese) [李鹤龄, 王娟娟, 杨斌, 沈宏君 2015 64 040501]
[34] Dehmelt H 1988 Phys. Scr. T22 102
[35] Curtis, Lorenzo J 2003 Atomic Structure and Lifetime: A Conceptual Approach (Cambridge: Cambridge University Press) p74
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