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量子相空间纠缠轨线力学

徐峰 郑雨军

量子相空间纠缠轨线力学

徐峰, 郑雨军
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  • 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.
    • 基金项目: 国家自然科学基金 (批准号: 21073110) 资助的课题.
    [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)]

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    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]

    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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出版历程
  • 收稿日期:  2013-06-18
  • 修回日期:  2013-07-27
  • 刊出日期:  2013-11-05

量子相空间纠缠轨线力学

  • 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.

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.

English Abstract

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