混沌微扰导致的量子退相干

赵文垒; 王建忠; 豆福全

doi:10.7498/aps.61.240302

摘要

研究了无限深势阱内两个粒子的耦合导致的量子退相干和量子行为趋近于经典混沌运动的过程. 当一个粒子的质量减小时,它对另外一个粒子经典混沌扩散的影响逐渐减小. 强混沌机理使得轻粒子的作用类似于噪声, 从而有效得抑制另外一个粒子的量子相干性. 轻粒子的退相干效应随着有效普朗克常数的减小逐渐增强. 在这个过程中, 另外一个粒子的量子扩散从动力学局域化行为逐渐过渡到经典极限. 当有效普朗克常数足够小时, 它的量子扩散与经典混沌扩散相符合. 该粒子的线性墒随时间演化迅速趋近于饱和值, 并且饱和值随着有效普朗克常数减小以指数函数形式从零趋近于1.

关键词:

Abstract

Via a system of two kicked particles that are coupled in an infinite square well, we numerically show that the interaction with a particle of very small mass is able to lead to a quantum-to-classical transition on condition that the corresponding classical dynamics is almost unaffected. With the decrease of the mass of one of the particles, its effect on the classical dynamics of the other one decreases. Such an effect is even negligible if the mass of the particle is small enough. The classically chaotic dynamics of this small particle is effective for promoting the decoherence of the heavy particle. Therefore its quantum behavior exhibits the transition from the dynamical localization to the classically chaotic diffusion with the decrease of the effective Planck's constant ħ. Under the perturbation from the small particle, the linear entropy is rapidly saturated as time passes by. With the decrease of ħ, the time-averaged linear entropy exponentially increases from zero to almost unity.

Keywords:

作者及机构信息

1.
北京理工大学物理学院, 北京 100081;

2.
北京应用物理与计算数学研究所, 计算物理国家重点实验室, 北京 100088;

3.
北京大学应用物理与技术研究中心, 高能量密度物理数值模拟教育部重点实验室, 北京 100084

基金项目: 国家高技术研究发展计划(863计划) (批准号: 2011AA120101)和国家重点基础研究发展计划(973计划) (批准号: 2011CB921503)资助的课题.

Authors and contacts

1.
School of Physics, Beijing Institute of Technology, Beijing 100081, China;

2.
National Key Laboratory of Science and Technology on Computation Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;

3.
HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100084, China

Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2011AA120101), and the National Basic Research Program of China (Grant No. 2011CB921503).

参考文献

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[13]	Graham R, Kolovsky A R 1996 Phys. Lett. A 222 47
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施引文献

[1]	Joos 2003 Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin)
[2]	Zurek W H 2003 Rev. Mod. Phys. 75 715
[3]	Schlosshauer M 2004 Rev. Mod. Phys. 76 1267Schlosshauer M 2008 Found. Phys. 38 796
[4]	Pattanayak A K, Sundaram B, Greenbaum B D 2003 Phys. Rev. Lett. 90 014103
[5]	Feynman R P, Vernon F L 1963 Ann. Phys. (Leipzig) 24 118
[6]	Caldeira A O, Leggett A J 1983 Physica (Amsterdam) 121A 587
[7]	Wisniacki D, Toscano F 2009 Phys. Rev. E 79 025203(R)
[8]	Toscano F, De Matos Filho R L, Davidovich L 2005 Phys. Rev. A 71 010101(R)
[9]	Toscano F, Wisniacki D A 2006 Phys. Rev. E 74 056208
[10]	Rossini D, Benenti G, Casati G 2006 Phys. Rev. E 74 036209
[11]	Bandyopadhyay J N 2009 EPL 85 50006
[12]	Adachi S, Toda M, Ikeda K 1988 Phys. Rev. Lett. 61 659
[13]	Graham R, Kolovsky A R 1996 Phys. Lett. A 222 47
[14]	Park H K, Kim S W 2003 Phys. Rev. A 67 060102(R)
[15]	Petitjean C, Jacquod Ph 2006 Phys. Rev. Lett. 97 194103
[16]	Jie Q L, Hu B, Dong G 2006 arXiv:quantph/ 0601025
[17]	Liu J, Cheng W T, Cheng C G 2000 Commun. Theor. Phys. 33 15Liu J, Hu B, Li B 1998 Phys. Rev. Lett. 81 1749
[18]	Hu B, Li B, Liu J, Gu Y 1999 Phys. Rev. Lett. 82 4224
[19]	Izrailev F M 1990 Phys. Rep. 196 299Fishman S, Grempel D R, Prange R E 1982 Phys. Rev. Lett. 49 509
[20]	Shepelyansky D L 1986 Phys. Rev. Lett. 56 677Shepelyansky D L 1987 Physica D 28 103
[21]	Casati G, Chirikov B V, Izraelev F M, Ford J 1979 Stochastic Behavior in Classical and Quantum Hamiltonian Systems, edited by Casati G and Ford J, Lecture Notes in Physics (Vol. 93) (Springer, Berlin)
[22]	Lakshminarayan A 2001 Phys. Rev. E 64 036207Bandyopadhyay J N, Lakshminarayan A 2002 Phys. Rev. Lett. 89 060402
[23]	Cohen D, Heller E J 2000 Phys. Rev. Lett. 84 2841
[24]	Wisniacki D A, Cohen D 2002 Phys. Rev. E 66 046209
[25]	Wisniacki D A, Ares N, Vergini E G 2010 Phys. Rev. Lett. 104 254101

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