介观RLC电路的密度矩阵的量子耗散

范洪义; 何锐

doi:10.7498/aps.63.110301

摘要

本文首次采用求解密度矩阵的振幅衰减主方程来研究介观RLC电路的量子耗散. 我们考虑到电路实际上处在热环境中，就尝试用（经约化了热库自由度以后）密度矩阵的振幅耗散主方程来研究介观RLC电路的量子衰减，即将电路看作是一个哈密顿稳态系统（不显含时），而该系统对应的密度矩阵是处在振幅耗散通道中（耗散系数由回路的品质因数决定）随着时间演化，我们求出该回路密度矩阵的量子耗散及回路能量的衰减规律. 我们采用纠缠态表象和有序算符内的积分（求和）技术探讨此问题，可以给出终态密度矩阵的解析形式，具有简捷的特点.

关键词:

Abstract

For the first time, as far as we know, we use the approach of solving the amplitude-decaying master equation of density matrix to study the quantum dissipation of a mesoscopic RLC circuit, and thus find out the attenuation law of circuit energy. We then use the entangled state representation and the technique of integration within an ordered product of operators to explore this problem.

Keywords:

作者及机构信息

范洪义,
何锐

1.
中国科学技术大学材料科学与工程系, 合肥 230026

基金项目: 国家自然科学基金（批准号：11175113）和中央高校基本科研业务费专项资金（批准号：WK2060140013）资助的课题.

Authors and contacts

Fan Hong-Yi,
He Rui

1.
Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11175113), and the Fundamental Research Funds for the Central Universities of China (Grant No. WK2060140013).

参考文献

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[5]	Song T Q 2003 Int. J. Theor. Phys. 42 793
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[13]	Fan H Y, Pan X Y 1998 Chin. Phys. Lett. 15 625
[14]	Xu C L 2012 Chin. Phys. B 21 020402
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[16]	Fan H Y, Xu X X, Hu L Y 2010 Chin. Phys. B 19 060502
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[21]	Xie Y X, Li Z J, Zhou G H 2007 Acta. Phys. Sin. 56 7224 (in Chinese)[谢月新, 李志坚, 周光辉 2007 物理学报 56 7224]
[22]	Long C Y 2003 Acta. Phys. Sin. 52 2033 (in Chinese)[龙超云 2003 物理学报 52 2033]
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[25]	Fan H Y, Hu L Y 2008 Opt. Commun. 281 5571
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[27]	Fan H Y, Hu L Y 2009 Opt. Commun. 282 932
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[29]	Fan H Y, Hu L Y 2008 Mod. Phys. Lett. B 22 2435
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[31]	Fan H Y, Vanderlinde J 1989 Phys. Rev. A 39 1552
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[33]	Fan H Y 1990 Phys. Rev. A 41 1526
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[35]	Hu L Y, Fan H Y 2009 Chin. Phys. Lett. 26 090307
[36]	Hu L Y, Fan H Y 2009 Commun. Theor. Phys. 51 321
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[38]	Wei U 1999 Quantum Dissipative System (Singapore: World Scientific)
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[41]	Fan H Y 1991 Phys. Lett. A 161 1

施引文献

[1]	Louisell W H 1973 Quantum Statistical Properties of Radiation (New York: John Wiley)
[2]
[3]	Fan H Y, Liang X T 2000 Chin. Phys. Lett. 17 174
[4]
[5]	Song T Q 2003 Int. J. Theor. Phys. 42 793
[6]
[7]	Wang J S, Liu T K, Zhan M S 2000 Chin. Phys. Lett. 17 528
[8]	Xu X L, Li H Q, Wang J S 2006 Int. J. Theor. Phys. 45 2517
[9]
[10]
[11]	Wang J S, Sun C Y 1998 Int. J. Theor. Phys. 37 1213
[12]
[13]	Fan H Y, Pan X Y 1998 Chin. Phys. Lett. 15 625
[14]	Xu C L 2012 Chin. Phys. B 21 020402
[15]
[16]	Fan H Y, Xu X X, Hu L Y 2010 Chin. Phys. B 19 060502
[17]
[18]
[19]	Xu X L, Li H Q, Wang J S 2007 Chin. Phys. 16 2462
[20]
[21]	Xie Y X, Li Z J, Zhou G H 2007 Acta. Phys. Sin. 56 7224 (in Chinese)[谢月新, 李志坚, 周光辉 2007 物理学报 56 7224]
[22]	Long C Y 2003 Acta. Phys. Sin. 52 2033 (in Chinese)[龙超云 2003 物理学报 52 2033]
[23]
[24]
[25]	Fan H Y, Hu L Y 2008 Opt. Commun. 281 5571
[26]
[27]	Fan H Y, Hu L Y 2009 Opt. Commun. 282 932
[28]
[29]	Fan H Y, Hu L Y 2008 Mod. Phys. Lett. B 22 2435
[30]
[31]	Fan H Y, Vanderlinde J 1989 Phys. Rev. A 39 1552
[32]
[33]	Fan H Y 1990 Phys. Rev. A 41 1526
[34]
[35]	Hu L Y, Fan H Y 2009 Chin. Phys. Lett. 26 090307
[36]	Hu L Y, Fan H Y 2009 Commun. Theor. Phys. 51 321
[37]
[38]	Wei U 1999 Quantum Dissipative System (Singapore: World Scientific)
[39]
[40]
[41]	Fan H Y 1991 Phys. Lett. A 161 1

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