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Using the quantum phase space technique and the information-theory like the Wehrl entropy, the Husimi function and the Wehrl entropy of the quantum pure states and the corresponding mixed states in thermo field dynamics are studied. It is found that the Husimi function and the Wehrl entropy of the thermal coherent state agree with that of the corresponding mixed states. And the Wehrl entropy of thermal coherent state is not related with the displacement factor. Therefore for a quantum system, the quantum fluctuations of the observable quantities and corresponding uncertainty relation are also not related with the displacement factor in the thermal coherent state.
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Keywords:
- thermo field dynamics /
- Husimi function /
- Wehrl entropy
[1] ［1］Takahashi Y, Umezawa H 1975 Collective Phenomena 2 55
[2] ［2］Fearn H, Collett M J 1988 J. Mod. Opt. 35 553
[3] ［3］Oz-Vogt J, Mann A, Revzen M 1991 J. Mod. Opt. 38 2339
[4] ［4］Fan H Y, Liang X T 2000 Chin. Phys. Lett. 17 174
[5] ［5］Wang Z Q 2002 Acta Phys. Sin. 51 1808（in Chinese）［汪仲清 2002 51 1808］
[6] ［6］Zhan Y B 2004 Chin. Phys. 13 234
[7] ［7］Li H Q, Xu X L, Wang J S 2006 Chin. Phys. Lett. 23 2892
[8] ［8］Xu X L, Li H Q, Wang J S 2007 Chin. Phys. 16 2462
[9] ［9］Mintert F,Zyczkowski K 2004 Phys. Rev.A 69 2317
[10] ］Fan H Y 1991 Commun. Theor. Phys. 16 123
[11] ］Wang S 2009 Acta Optica Sinica 29 1101 （in Chinese）［王帅 2009 光学学报 29 1101 ］
[12] ］Meng X G, Wang J S, Liang B L 2007 Acta Phys. Sin. 56 2160（in Chinese）［孟祥国、王继锁、梁宝龙 2007 56 2160］
[13] ］Husimi K 1940 Proc. Phys. Math. Soc. Japan. 22 264
[14] ］Anderson A, Halliwell J J 1993 Phys. Rev. D 48 2753
[15] ］Pennini F, Plastino A 2004 Phys. Rev. E69 7101
[16] ］Xu X W, Ren T Q, Chi Y J, Zhu Y L, Liu S Y 2006 Acta Phys. Sin. 55 3892（in Chinese）［徐秀玮、任廷琦、迟永江、朱友良、刘姝廷 2006 55 3892］
[17] ］Glauber R J 1963 Phys. Rev. 131 2766
[18] ］Fan H Y 2005 From Quantum Mechanics to Quantum Optics（Shanghai: Shanghai Jiaotong University Press）（in Chinese）［范洪义 2005 从量子力学到量子光学（上海:上海交通大学出版社）］
[19] ］Wehrl A 1978 Rev. Mod. Phys. 50 221
[20] ］Department of Physics, Peking University 1987 Quantum Statistical Physics（Beijing: Peking University Press）p28（in Chinese）［北京大学物理系《量子统计物理学》编写组 1987 量子统计物理学（北京: 北京大学出版社）第28页］
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[1] ［1］Takahashi Y, Umezawa H 1975 Collective Phenomena 2 55
[2] ［2］Fearn H, Collett M J 1988 J. Mod. Opt. 35 553
[3] ［3］Oz-Vogt J, Mann A, Revzen M 1991 J. Mod. Opt. 38 2339
[4] ［4］Fan H Y, Liang X T 2000 Chin. Phys. Lett. 17 174
[5] ［5］Wang Z Q 2002 Acta Phys. Sin. 51 1808（in Chinese）［汪仲清 2002 51 1808］
[6] ［6］Zhan Y B 2004 Chin. Phys. 13 234
[7] ［7］Li H Q, Xu X L, Wang J S 2006 Chin. Phys. Lett. 23 2892
[8] ［8］Xu X L, Li H Q, Wang J S 2007 Chin. Phys. 16 2462
[9] ［9］Mintert F,Zyczkowski K 2004 Phys. Rev.A 69 2317
[10] ］Fan H Y 1991 Commun. Theor. Phys. 16 123
[11] ］Wang S 2009 Acta Optica Sinica 29 1101 （in Chinese）［王帅 2009 光学学报 29 1101 ］
[12] ］Meng X G, Wang J S, Liang B L 2007 Acta Phys. Sin. 56 2160（in Chinese）［孟祥国、王继锁、梁宝龙 2007 56 2160］
[13] ］Husimi K 1940 Proc. Phys. Math. Soc. Japan. 22 264
[14] ］Anderson A, Halliwell J J 1993 Phys. Rev. D 48 2753
[15] ］Pennini F, Plastino A 2004 Phys. Rev. E69 7101
[16] ］Xu X W, Ren T Q, Chi Y J, Zhu Y L, Liu S Y 2006 Acta Phys. Sin. 55 3892（in Chinese）［徐秀玮、任廷琦、迟永江、朱友良、刘姝廷 2006 55 3892］
[17] ］Glauber R J 1963 Phys. Rev. 131 2766
[18] ］Fan H Y 2005 From Quantum Mechanics to Quantum Optics（Shanghai: Shanghai Jiaotong University Press）（in Chinese）［范洪义 2005 从量子力学到量子光学（上海:上海交通大学出版社）］
[19] ］Wehrl A 1978 Rev. Mod. Phys. 50 221
[20] ］Department of Physics, Peking University 1987 Quantum Statistical Physics（Beijing: Peking University Press）p28（in Chinese）［北京大学物理系《量子统计物理学》编写组 1987 量子统计物理学（北京: 北京大学出版社）第28页］
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