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

[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)

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)

[1]	黄文逍, 张逸竹, 阎天民, 江玉海. 超快强场下低能光电子的研究进展解析R矩阵半经典轨迹理论. , 2016, 65(22): 223204. doi: 10.7498/aps.65.223204
[2]	段志欣, 邱明辉, 姚翠霞. 采用量子波包方法和准经典轨线方法研究S(3P)+HD反应. , 2014, 63(6): 063402. doi: 10.7498/aps.63.063402
[3]	徐国亮, 刘培, 刘彦磊, 张琳, 刘玉芳. 准经典轨线法研究交换反应H(D)+SH/SD的动力学性质. , 2013, 62(22): 223402. doi: 10.7498/aps.62.223402
[4]	李红, 郑斌, 孟庆田. 转动激发对O+HBrOH+Br反应的立体动力学性质的准经典轨线理论研究. , 2012, 61(15): 153401. doi: 10.7498/aps.61.153401
[5]	王平. C+OH(v=0—3, j=0—3)→CO+H反应的准经典轨线研究. , 2011, 60(5): 053401. doi: 10.7498/aps.60.053401
[6]	张晓燕, 王继锁. 相空间中对称的纠缠相干态及其非经典特性. , 2011, 60(9): 090304. doi: 10.7498/aps.60.090304
[7]	邓善红, 高嵩, 李永平, 裴云昌, 林圣路. 平行电磁场中锂原子自电离的半经典分析. , 2010, 59(2): 826-831. doi: 10.7498/aps.59.826
[8]	高嵩, 徐学友, 周慧, 张延惠, 林圣路. 电场中里德伯原子动力学性质的半经典理论研究. , 2009, 58(3): 1473-1479. doi: 10.7498/aps.58.1473
[9]	王墨戈, 陆启生, 许晓军, 郭少锋. 宽谱染料激光器的数值模型及实验验证. , 2008, 57(3): 1857-1861. doi: 10.7498/aps.57.1857
[10]	何志红, 姚建铨, 时华峰, 黄晓, 罗锡璋, 江绍基, 李建荣, 王鹏. 抽运光强度对光学抽运重水气体产生THz激光的影响分析. , 2007, 56(11): 6451-6456. doi: 10.7498/aps.56.6451
[11]	何志红, 姚建铨, 时华锋, 黄晓, 罗锡璋, 江绍基, 王鹏. 光泵重水气体产生THz激光的半经典理论分析. , 2007, 56(10): 5802-5807. doi: 10.7498/aps.56.5802
[12]	欧阳世根, 关毅, 佘卫龙. 旋转超导体中的电流与电磁场. , 2002, 51(7): 1596-1599. doi: 10.7498/aps.51.1596
[13]	张飞舟, 王矫, 顾雁. 量子混沌系统本征态的统计非遍历性及其半经典极限. , 1999, 48(12): 2169-2179. doi: 10.7498/aps.48.2169
[14]	布和, 刘辽. 半经典Brans-Dicke理论中的闭合宇宙解. , 1998, 47(5): 728-731. doi: 10.7498/aps.47.728
[15]	李治宽. Raman自由电子激光的半经典理论. , 1996, 45(11): 1812-1816. doi: 10.7498/aps.45.1812
[16]	王海达. 氩气直流放电等离子体中三稳现象的半经典理论. , 1990, 39(12): 1928-1936. doi: 10.7498/aps.39.1928
[17]	张建平, 李玲, 叶培大. 电负反馈半导体激光器半经典理论. , 1989, 38(9): 1436-1442. doi: 10.7498/aps.38.1436
[18]	陈天杰. 位相因子在光学量子拍的半经典解释中的作用. , 1986, 35(12): 1652-1656. doi: 10.7498/aps.35.1652
[19]	潘少华, 韩全生. 分布反馈染料激光器的半经典理论. , 1982, 31(3): 318-327. doi: 10.7498/aps.31.318
[20]	潘少华. 染料激光器模式耦合半经典理论. , 1981, 30(8): 1067-1076. doi: 10.7498/aps.30.1067

计量

文章访问数: 6610
PDF下载量: 1653
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板