量子相空间纠缠轨线力学

徐峰; 郑雨军

doi:10.7498/aps.62.213401

摘要

量子相空间理论已用来研究物理学、化学等有关问题, 并为人们研究经典物理和量子物理的对应关系提供了一种有力工具. 在量子相空间中, 基于Wigner表象下的量子刘维尔方程, 建立分子纠缠轨线力学. 与经典分子力学方法不同, 分子纠缠轨线力学中的轨线不再是独立的, 而是纠缠在一起的, 这正是体系量子效应的体现. 这种半经典的理论方法能给出体系的量子效应及具有启示意义的物理图像. 分子纠缠轨线力学被用来研究量子隧穿效应、分子光解反应动力学、自关联函数等. 本文综述了分子纠缠轨线力学最近的发展.

关键词:

Abstract

Quantum phase space theory is widely used to investigate physical, and chemical questions. It gives us a powerful tool to study the relations between the classical and quantum world. In quantum phase space theory, entangled molecular dynamics method is developed based on quantum Liouville equation. It is different from classical Hamilton dynamics, the trajectories are entangled i.e. not independent with each other. The quantum effect in the system can be described using the semiclassical theory, and give a vivid physical picture. The quantum tunneling, photodissociation, and self-correlation are investigated using the entangled trajectory. In this paper, we review the recent development in this field.

Keywords:

作者及机构信息

徐峰,
郑雨军

1.
山东大学物理学院, 济南 250100

基金项目: 国家自然科学基金 (批准号: 21073110) 资助的课题.

Authors and contacts

1.
School of Physics, Shandong University, Jinan 250100, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.21073110).

参考文献

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[58]	Zhang X F, Zheng Y 2009 Chin. Phys. Lett 26 023404
[59]	Wang L, Marten C C, Zheng Y 2012 J. Chem. Phys. 137 034113
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[62]	Sala R, Brouard S, Muga J G 1993 J. Chem. Phys. 99 2708
[63]	Zhang S, Pollak E 2004 J. Chem. Phys. 121 3384
[64]	Silverman B W 1986 Density Estimation for Statistics and Data Analysis (London: Chapman and Hall)
[65]	Fukunaga K 1986 Introduction to Statistical Pattern Recognition (San Diego: Academic, 2nd)
[66]	Martens C C, Zheng Y J 2013 personal communication
[67]	Nauenberg M 1989 Phys. Rev. A 40 1133
[68]	Barnes I M, Nauenberg M, Nockleby M, Tomsovic S 1993 Phys. Rev. Lett. 71 1961
[69]	Tomsovic S, Lefebvre J H 1997 Phys. Rev. Lett. 79 3629
[70]	Yeazell J A, Stroud C R 1991 Phys. Rev. A 43 5153
[71]	Wals J, Fielding H H, Christian J F, Snoek L C, Zande W J, Linden H B 1994 Phys. Rev. Lett. 73 3783
[72]	Zdanska P, Moiseyev N 2001 J. Phys. Chem. 115 10608
[73]	Wang L, Wang Y, Ran S, Yang G 2009 J. Electron Spectrosc. Relat. Phenom. 173 40
[74]	Tannor D J 2006 Introduction to Quantum Mechanics A Time-Dependent Perspective (USA: University Science Books)
[75]	Goldfarb Y, Tannor D J 1996 Chem. Phys. Lett. 263 324
[76]	Wang L F, Zheng Y J 2013 Chem. Phys. Lett 563 112
[77]	Engel V, Schinke R, Staemmler V 1988 J. Chem. Phys. 88 129
[78]	Kuhl K, Schinke R 1989 Chem. Phys. Lett. 158 81
[79]	Zhang J Z, Imre D G 1989 J. Chem. Phys. 90 1666
[80]	Brouard M, Langford S R 1994 J. Chem. Phys. 101 7458
[81]	Schinke R, Staemmler V, Wal R L V, Crion F F, Sension R J, Hudson B, Andere-sen P, Silverman R 1992 J. Phys. Chem. 96 3201
[82]	Henriken N E, Engel V, Schinke R 1986 J. Phys. Chem. 86 6862
[83]	Hupper B E B, Engel V 1997 J. Phys. B 30 3191
[84]	Schinke R 1993 Photodissociation Dynamics (England: Cambridge University Press)

施引文献

[1]	Wigner E P 1932 Phys. Rev. 40 749
[2]	Glauber R J 1963 Phys. Rev. 130 2593
[3]	Glauber R J 1963 Phys. Rev. 131 2766
[4]	Moyal J E 1949 Proc. Cambrridge. Philos. Soc. 45 99
[5]	Lee H W, Scully M O 1983 Found. Phys. 13 61
[6]	Carruthers P, Zachariasen F 1983 Rev. Mod. Phys. 55 245
[7]	Berry M V 1977 Phil. Trans. R. Soc. A 287 237
[8]	Takahashi K 1989 Prog. Theor. Phys. Suppl. 98 109
[9]	Mahmud K W, Perry H, Reinhardt W P 2005 Phys. Rev. A 71 023615
[10]	Shuai Z G, Shao J S 2008 Theoretical chemistry and application (Beijing: Science Press) (in Chinese) [帅志刚, 邵久书 2008 理论化学原理和运用 (北京: 科学出版社)]
[11]	Allen M P 1987 Computer Simulation of Liquids (Oxford: Clarendon Press)
[12]	Heller E J 1991 J. Chem. Phys. 94 2723
[13]	Li Z, Zadoyan R, Apkarian V A, Martens C C 1995 J. Chem. Phys. 99 7453
[14]	Lee H W, Scully M O 1980 J. Chem. Phys. 73 2238
[15]	Geyer T, Rost J M 2002 J. Phys. B 35 1479
[16]	Sheppard M G, Walker R B 1983 J. Chem. Phys. 78 7191
[17]	Henriksen N E 1985 Chem. Phys. Lett. 121 139
[18]	Li Q, Wei Q, Lu L 2004 Phys. Rev. A 70 022105
[19]	Heller E J 1976 J. Chem. Phys. 65 1289
[20]	Heller E J 1981 J. Chem. Phys. 67 3339
[21]	Brown R C, Heller E J 1981 J. Chem. Phys. 75 186
[22]	Zhang D, Chu T S, Hao C 2013 Chin. Phys. B 22 063401
[23]	Bohm D 1952 Phys. Rev. 85 166
[24]	Bohm D 1952 Phys. Rev. 85 180
[25]	Miller W H 2001 J. Phys. Chem. A 105 2942
[26]	Pollak E, Shao J 2003 J. Phys. Chem. A 107 7112
[27]	Donoso A, Martens C C 2001 Phys. Rev. Lett. 87 223202
[28]	Li Q S, Hu X G 2000 Reaction scattering theory in quantum phase space (Beijing: Science Press) (in Chinese) [李前树, 胡旭光 2003 量子相空间中的反应散射理论 (北京: 科学出版社)]
[29]	Shewell J R 1959 Amer. J. Phys. 27 17
[30]	Mehta C L 1964 J. Math. Phys. 5 677
[31]	Mehta C L, Sudarshan E C G 1965 Phys. Rev. B 138 274
[32]	Cohen L 1966 J. Math. Phys. 7 781
[33]	Agarwal G S, Wolf E 1968 Phys. Rev. Lett. 21 180
[34]	Cahill K E, Glauber R J 1969 Phys. Rev. 177 1857
[35]	Cahill K E, Glauber R J 1969 Phys. Rev. 177 1882
[36]	Heller E J 1991 J. Chem. Phys. 94 2723
[37]	Broglie L De 1926 C. R. Acad. Sci. Pairs. 183 447
[38]	Broglie L De 1927 C. R. Acad. Sci. Pairs. 184 273
[39]	Madelung E 1926 Z. Phys. 40 332
[40]	Zurek W H, Wheeler J A 1983 Quantum Theory and Measurement (Princeton NJ: Princeton University Press)
[41]	Sanz A S, Borondo F, Miret-Artes S 2000 Phys. Rev. B 61 7743
[42]	Sanz A S, Borondo F, Miret-Artes S 2004 Phys. Rev. B 69 115413
[43]	Guantes R, Sanz A S, Margalef J R, Miret-Artes S 2004 Surf. Sci. Rep. 53 199
[44]	Sanz A S, Miret-Artes S 2007 J. Chem. Phys. 126 234106
[45]	Sanz A S, Miret-Artes S 2007 Chem. Phys. Lett. 445 350
[46]	Wyatt R E 2005 Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics (New York: Springer Press)
[47]	Chou C C, Wyatt R E 2006 J. Chem. Phys. 125 174103
[48]	Chou C C, Wyatt R E 2008 J. Chem. Phys. 128 154106
[49]	Chou C C, Wyatt R E 2008 J. Chem. Phys. 129 124113
[50]	Chou C C, Sanz A S, Miret-Artes S, Wyatt R E 2009 Phys. Rev. Lett. 102 250401
[51]	Chou C C, Wyatt R E 2012 Ann. Phys. 327 1355
[52]	Lai X Y, Cai Q Y, Zhan M S 2010 Chin. Phys. B 19 020302
[53]	Donoso A, Zheng Y, Martens C C 2003 J. Chem. Phys. 119 5010
[54]	Donoso A, Martens C C 2010 Chem. Phys. 370 20
[55]	Hogan P, Wart A A, Donoso A, Martens C C 2002 J. Chem. Phys. 116 10598
[56]	Lopez H, Martens C C, Donoso A 2006 J. Chem. Phys. 125 154111
[57]	Wang A S, Zheng Y, Martens C C, Ren W Y 2009 Phys. Chem. Chem. Phys. 11 1588
[58]	Zhang X F, Zheng Y 2009 Chin. Phys. Lett 26 023404
[59]	Wang L, Marten C C, Zheng Y 2012 J. Chem. Phys. 137 034113
[60]	Xu F, Wang L, Marten C C, Zheng Y 2013 J. Chem. Phys. 138 024113
[61]	Wang L, Xu F, Zheng Y 2013 J. At. & Mol. Sci. (in press)
[62]	Sala R, Brouard S, Muga J G 1993 J. Chem. Phys. 99 2708
[63]	Zhang S, Pollak E 2004 J. Chem. Phys. 121 3384
[64]	Silverman B W 1986 Density Estimation for Statistics and Data Analysis (London: Chapman and Hall)
[65]	Fukunaga K 1986 Introduction to Statistical Pattern Recognition (San Diego: Academic, 2nd)
[66]	Martens C C, Zheng Y J 2013 personal communication
[67]	Nauenberg M 1989 Phys. Rev. A 40 1133
[68]	Barnes I M, Nauenberg M, Nockleby M, Tomsovic S 1993 Phys. Rev. Lett. 71 1961
[69]	Tomsovic S, Lefebvre J H 1997 Phys. Rev. Lett. 79 3629
[70]	Yeazell J A, Stroud C R 1991 Phys. Rev. A 43 5153
[71]	Wals J, Fielding H H, Christian J F, Snoek L C, Zande W J, Linden H B 1994 Phys. Rev. Lett. 73 3783
[72]	Zdanska P, Moiseyev N 2001 J. Phys. Chem. 115 10608
[73]	Wang L, Wang Y, Ran S, Yang G 2009 J. Electron Spectrosc. Relat. Phenom. 173 40
[74]	Tannor D J 2006 Introduction to Quantum Mechanics A Time-Dependent Perspective (USA: University Science Books)
[75]	Goldfarb Y, Tannor D J 1996 Chem. Phys. Lett. 263 324
[76]	Wang L F, Zheng Y J 2013 Chem. Phys. Lett 563 112
[77]	Engel V, Schinke R, Staemmler V 1988 J. Chem. Phys. 88 129
[78]	Kuhl K, Schinke R 1989 Chem. Phys. Lett. 158 81
[79]	Zhang J Z, Imre D G 1989 J. Chem. Phys. 90 1666
[80]	Brouard M, Langford S R 1994 J. Chem. Phys. 101 7458
[81]	Schinke R, Staemmler V, Wal R L V, Crion F F, Sension R J, Hudson B, Andere-sen P, Silverman R 1992 J. Phys. Chem. 96 3201
[82]	Henriken N E, Engel V, Schinke R 1986 J. Phys. Chem. 86 6862
[83]	Hupper B E B, Engel V 1997 J. Phys. B 30 3191
[84]	Schinke R 1993 Photodissociation Dynamics (England: Cambridge University Press)

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