English
往期目录
新闻公告
More
化学进展 2012, Vol. 24 Issue (06): 1129-1152 前一篇   后一篇

• 量子化学专辑 •

量子耗散与量子输运的级联方程组方法

郑晓1, 徐瑞雪1, 许健2, 金锦双3, 胡洁2,4, 严以京*1,2   

  1. 1. 中国科学技术大学合肥微尺度物质科学国家实验室(筹) 合肥 230026;
    2. 香港科技大学化学系 香港;
    3. 杭州师范大学物理系 杭州 310026;
    4. 首都师范大学物理学院 北京 100048
  • 收稿日期:2011-12-01 修回日期:2012-03-01 出版日期:2012-06-24 发布日期:2012-05-11
  • 通讯作者: 严以京 E-mail:yyan@ust.hk
下载PDF ( 1475 ) 引用
导出 被引次数 ( 2 )

Hierarchical Equations of Motion for Quantum Dissipation and Quantum Transport

Zheng Xiao1, Xu Ruixue1, Xu Jian2, Jin Jinshuang3, Hu Jie2,4, Yan Yijing1,2   

  1. 1. Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China; 1.Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026,China;
    2. Department of Chemistry,Hong Kong University of Science and Technology, Kowloon, Hong Kong;
    3. Department of Physics, Hangzhou Normal University, Hangzhou 310036, China;
    4. School of Physics, Capital normal university, Beijing 100048, China
  • Received:2011-12-01 Revised:2012-03-01 Online:2012-06-24 Published:2012-05-11
级联方程已成为研究量子开放系统的稳态性质和动力学过程的重要方法。本文旨在系统综述量子耗散和量子输运的级联方程组方法的建立、发展以及在理论、算法和应用方面的一些最新进展。级联方程形式理论的建立以影响泛函路径积分为基础,并具有数值上的高效性和应用上的灵活性,可用于研究分子体系的复杂动力学过程以及强关联电子体系中的量子输运。其级联耦合结构以非微扰的方式揭示了多体相互作用、体系-环境耦合、非马尔可夫记忆等的综合效应。作为应用示例,我们采用级联方程模拟了生物光富集体系的二维相干动力学光谱以及含时电子输运过程中的动态近藤效应。
关键词： 量子耗散, 量子输运, 开放体系, 级联方程组
In this review we give a comprehensive account of a hierarchical equations of motion (HEOM) approach to the characterization ofstationary and dynamic properties of open quantum systems.This approach is rooted at the Feynman-Vernon influence functional path integral formalism, but much more implementable numerically and operationally for the study of various complex molecular dynamics and quantum transport in strongly correlated electronic systems.By construction, HEOM resolves nonperturbatively the combined effects of many-particle interaction, system-bath coupling,and non-Markovian memory.Finally the practicality of HEOM to address physical and chemical problems is exemplified with a model simulation of coherent two-dimensional spectroscopy signals of a biological light-harvesting system and a time-dependent quantum transport system involving dynamic Kondo transition.
Key words: quantum dissipation, quantum transport, open system, hierarchical equation of notion (HEOM)

中图分类号: 

()
[1] Engel G S, Calhoun T R, Read E L, Ahn T K, Man al T, Cheng Y C, Blankenship R E, Fleming G R. Nature, 2007, 446: 782-86
[2] Lee H, Cheng Y C, Fleming G R. Science, 2007, 316: 1462-1465
[3] Calhoun T R, Ginsberg N S, Schlau-Cohen G S, Cheng Y C, Ballottari M, Bassi R, Fleming G R. J. Phys. Chem. B, 2009, 113: 16291-16295
[4] Panitchayangkoon G, Hayes D, Fransted K A, Caram J R, Harel E, Wen J, Blankenship R E, Engel G S. Proc. Natl. Acad. Sci. USA, 2010, 107: 12766-12770
[5] Collini E, Wong C Y, Wilk K E, Curmi P M G, Brumer P, Scholes G D. Nature, 2010, 463: 644-647
[6] Blankenship R E. Molecular Mechanisms of Photosyn-thesis, BlackwellScience: Oxford, 2002
[7] Van Amerongen H, Valkunas L, van Grondelle R. Photosythetic Exictons, Singapore: World Scientic, 2000
[8] Ishizaki A, Fleming G R. J. Chem. Phys., 2009, 130: art. no. 234110.
[9] Ishizaki A, Fleming G R. J. Chem. Phys., 2009, 130: art. no. 234111.
[10] Tanimura Y. Phys., Rev., A, 1990, 41: 6676-6687
[11] Tanimura Y. J. Phys. Soc. Jpn., 2006, 75: art. no. 082001
[12] Yan Y A, Yang F, Liu Y, Shao J S. Chem. Phys. Lett., 2004, 395: 216-221
[13] Shao J S. J. Chem. Phys., 2004, 120: 5053-5056
[14] Xu R X, Cui P, Li X Q, Mo Y, Yan Y J. J. Chem. Phys., 2005, 122: art. no. 041103.
[15] Xu R X, Yan Y J. Phys. Rev. E, 2007, 75: art. no. 031107
[16] Jin J S, Zheng X, Yan Y J. J. Chem. Phys., 2008, 128: art. no. 234703
[17] Feynman R P, Vernon Jr F L. Ann. Phys., 1963, 24: 118-173
[18] Weiss U. Quantum Dissipative Systems, 3rd ed. Series in Modern Condensed Matter Physics, Singapore: World Scientific, 2008. Vol. 13
[19] Kleinert H. PathIntegrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 5th ed. Singapore: World Scientific, 2009
[20] Ishizaki A, Fleming G R. Proc. Natl. Acad. Sci. USA, 2009, 106: 17255-17260
[21] Xu J, Xu R X, Yan Y J. New J. Phys., 2009, 11: Singapore: art. no. 105037
[22] Shi Q, Chen L P, Nan G J, Xu R X, Yan Y J. J. Chem. Phys., 2009, 130: art. no. 164518
[23] Xu R X, Tian B L, Xu J, Shi Q, Yan Y J. J. Chem. Phys., 2009, 131: art. no. 214111
[24] Tanaka M, Tanimura Y. J. Chem. Phys., 2010, 132: art. no. 214502
[25] Ishizaki A, Tanimura Y. J. Chem. Phys., 2006, 125: art. no. 084501
[26] Ishizaki A, Tanimura Y. J. Phys. Chem. A, 2007, 111: 9269-9276
[27] Chen L P, Zheng R H, Shi Q, Yan Y J. J. Chem. Phys., 2010, 132: art. no. 024505
[28] Tian B L, Ding J J, Xu R X, Yan Y J. J. Chem. Phys., 2010, 133: art. no. 114112
[29] Ding J J, Xu J, Hu J, Xu R X, Yan Y J. J. Chem. Phys., 2011, 135: art. no. 164107
[30] Zhu K B, Xu R X, Zhang H Y, Hu J, Yan Y J. J. Phys. Chem. B, 2011, 115: 5678-5684
[31] Xu J, Xu R X, Abramavicius D, Zhang H D, Yan Y J. Chin. J. Chem. Phys., 2011, 24: 497-506
[32] Chen L P, Zheng R H, Jing Y Y, Shi Q. J. Chem. Phys., 2011, 134: art. no. 194508
[33] Hein B, Kreisbeck C, Kramer T, Rodr韌uez M. New J. Phys., 2012, 14: art. no. 023018
[34] Lu W, Ji Z, Pfeiffer L, West K W, Rimberg A J. Nature, 2003, 423: 422-425
[35] Lang N D, Avouris P. Phys. Rev. Lett., 2000, 84: 358-361
[36] Xue Y Q, Datta S, Ratner M A. Chem. Phys., 2002, 281: 151-170
[37] Taylor J, Guo H, Wang J. Phys. Rev. B, 2001, 63: art. no. 245407
[38] Ke S H, Baranger H U, Yang W T. Phys. Rev. B, 2004, 70: art. no. 085410
[39] Brandbyge M, Mozos J L, Ordej髇 P, Taylor J, Stokbro K. Phys. Rev. B, 2002, 65: art. no. 165401
[40] Yeyati A L, Mart? n-Rodero A, Flores F. Phys. Rev. Lett., 1993, 71: 2991-2994
[41] Datta S. Nanotechnology, 2004, 15: S433-S451
[42] Toher C, Filippetti A, Sanvito S, Burke K. Phys. Rev. Lett., 2005, 95: art. no. 146402
[43] Meir Y, Wingreen N S, Lee P A. Phys. Rev. Lett., 1993, 70: 2601-2604
[44] König J, Schoeller H, Schön G. Phys. Rev. Lett., 1996, 76: 1715-1718
[45] Kadanoff L P, Baym G. Quantum Statistical Mechanics, New York: Benjamin, 1962
[46] Dahlen N E, van Leeuwen R. Phys. Rev. Lett., 2007, 98: art. no. 153004
[47] Myöhänen P, Stan A, Stefanucci G, van Leeuwen R. Europhys. Lett., 2008, 84: art. no. 67001
[48] Bruder C, Schoeller H. Phys. Rev. Lett., 1994, 72: 1076
[49] Muralidharan B, Ghosh A W, Datta S. Phys. Rev. B, 2006, 73: art. no. 155410
[50] Pedersen J N, Wacker A. Phys. Rev. B, 2005, 72: art. no. 195330
[51] Weiss S, Eckel J, Thorwart M, Egger R. Phys. Rev. B, 2008, 77: art. no. 195316
[52] Horváth B, Lazarovits B, Sauret O, Zaránd G. Phys. Rev. B, 2008, 77: art. no. 113108
[53] Zheng X, Jin J S, Yan Y J. J. Chem. Phys., 2008, 129: art. no. 184112
[54] Zheng X, Jin J S, Yan Y J. New J. Phys., 2008, 10: art. no. 093016
[55] Zheng X, Luo J Y, Jin J S, Yan Y J. J. Chem. Phys., 2009, 130: art. no. 124508
[56] Jin J S, Welack S, Luo J Y, Li X Q, Cui P, Xu R X, Yan Y J. J. Chem. Phys., 2007, 126: art. no. 134113
[57] Zheng X, Jin J S, Welack S, Luo M, Yan Y J. J. Chem. Phys., 2009, 130: art. no. 164708
[58] Hu J, Xu R X, Yan Y J. J. Chem. Phys., 2010, 133: art. no. 101106
[59] Hu J, Luo M, Jiang F, Xu R X, Yan Y J. J. Chem. Phys., 2011, 134: art. no. 244106
[60] Shi Q, Chen L P, Nan G J, Xu R X, Yan Y J. J. Chem. Phys., 2009, 130: art. no. 084105
[61] Yan Y J, Xu R X. Annu. Rev. Phys. Chem., 2005, 56: 187-219
[62] Caldeira A O, Leggett A J. Ann. Phys., 1983, 149: 374-456, 153, 445(Erratum) (1984)
[63] Yan Y J. Phys. Rev. A, 1998, 58: 2721-2732
[64] Xu R X, Yan Y J. J. Chem. Phys., 2002, 116: 9196-9206
[65] Ding J J, Xu R X, Yan Y J. J. Chem. Phys., 2012, Submitted
[66] Ryder L H. Quantum Field Theory, 2nd ed, Cambridge: Cambridge University Press, 1996
[67] Press W H, Teukolsky S A, Vetterling W T, Flannery B P. Numerical Recipesin Fortran, New York : Cambridge University Press, 1992
[68] Croy A, Saalmann U. Phys. Rev. B, 2009, 80: art. no. 073102
[69] Xu J, Xu R X, Luo M, Yan Y J. Chem. Phys., 2010, 370: 109-114
[70] Baker Jr G A, Graves-Morris P. Pad? Approximants, 2nd ed. New York: Cambridge University Press, 1996
[71] Bulla R, Costi T A, Pruschke T. Rev. Mod. Phys., 2008, 80: 395
[72] Cheng Y C, Fleming G R. Annu. Rev. Phys. Chem., 2009, 60: 241-262
[73] Rebentrost P, Mohseni M, Kassal I, Lloyd S, Aspuru-Guzik A. New J. Phys., 2009, 11: art. no. 033003
[74] Rebentrost P, Shim S, Yuen-Zhou J, Aspuru-Guzik A. Procedia Chem., 2011, 3: 332-346
[75] Kim J H, Cao J S. J. Phys. Chem. B, 2010, 114: 16189-16197
[76] Wu J L, Liu F, Shen Y, Cao J S, Silbey R J. New J. Phys., 2010, 12: art. no. 105012
[77] Moix J, Wu J L, Huo P F, Coker D, Cao J S. J. Phys. Chem. Lett., 2011, 2: 3045-3052
[78] Mukamel S. Annu. Rev. Phys. Chem., 2000, 51: 691-729
[79] Abramavicius D, Palmieri B, Voronine D V, Sanda F, Mukamel S. Chem. Rev., 2009, 109: 2350-2408
[80] Mukamel S, Tanimura Y, Hamm P(Eds). Coherent Multidimensional Optical Spectroscopy, Special Issue of Acc. Chem. Res., 2009, 42(9): 1207-1469
[81] Cho M, Vaswani H M, Brixner T, Stenger J, Fleming G R. J. Phys. Chem. B, 2005, 109: 10542-10556
[82] F鑦e G, Mah? A, Berroir J M, Kontos T, Placcais B, Glattli D C, Cavanna A, Etienne B, Jin Y. Science, 2007, 316: 1169-1172
[83] Cui P, Li X Q, Shao J S, Yan Y J. Phys. Lett. A, 2006, 357: 449-453
[84] Li X Q, Yan Y J. Phys. Rev. B, 2007, 75: art. no. 075114
[85] Li G Q, Schreiber M, Kleinekathöfer U. Europhys. Lett., 2007, 79: art. no. 27006
[86] Jin J S, Zheng X, Yan Y J. AIP Conference Proceedings, 2008, 1074: 96-101
[87] Quantum Noise in Mesoscopic Physics, Nazarov Y V(Ed), Springer, 2003
[88] MacDonald D K C. Noise and Fluctuations: AnIn-troduction, New York: Wiley, 1962. Ch. 2. 2. 1.
[89] Deblock R, Onac E, Gurevich L, Kouwen-hoven L P. Science, 2003, 301: 203-206
[90] Aguado R, Kouwenhoven L P. Phys. Rev. Lett., 2000, 84: 1986-1989
[91] Wang S K, Jiao H, Li F, Li X Q, Yan Y J. Phys. Rev. B, 2007, 76: art. no. 125416
[92] Aguado R, Brandes T. Phys. Rev. Lett., 2004, 92: art. no. 206601
[93] Luo J Y, Li X Q, YanY J. Phys. Rev. B, 2007, 76: art. no. 085325
[94] Hanke U, Galperin Y M, Chao K A, Zou N. Phys. Rev. B, 1993, 48: 17209-17216
[95] Thielmann A, Hettler M H, König J, Schön G. Phys. Rev. B, 2003, 68: art. no. 115105
[96] Meir Y, Golub A. Phys. Rev. Lett., 2002, 88: art. no. 116802
[97] Ding G H, Ng T K. Phys. Rev. B, 1997, 56: art. no. R15521
[98] Hung K M, Wu G Y. Phys. Rev. B, 1993, 48: 14687-14689
[99] Chen L Y, Ting C S. Phys. Rev. B, 1991, 43: 4534-4537
[100] Anderson P W. Phys. Rev., 1961, 124: 41-53
[101] Shao J S, Zhou Y. Theoretical Chemistry: Principles and Applications (Shuai Z G, Shao J S, Eds), Beijing: Science Press, 2008. 511-550
[102] Kreisbeck C, Kramer T, Rodr韌uez M, Hein B. J. Chem. Theory Comput., 2011, 7: 2166-2174
[103] Runge E, Gross E K U. Phys. Rev. Lett., 1984, 52: 997-1000
[104] Zheng X, Chen G H, Mo Y, Koo S K, Tian H, Yam C Y, Yan Y J. J. Chem. Phys., 2010, 133: art. no. 114101
[105] Zheng X, Wang F, Yam C Y, Mo Y, Chen G H. Phys. Rev. B, 2007, 75: art. no. 195127
[106] Yam C Y, Mo Y, Wang F, Li X, Chen G H, Zheng X, Matsuda Y, W A GoddardIII J T. Nanotechnology, 2008, 19: art. no. 495203
[107] Wen S Z, Koo S K, Yam C Y, Zheng X, Yan Y J, Su Z M, Fan K N, Cao L, Wang W P, Chen G. J. Phys. Chem. B, 2011, 115: 5519-5525
[108] Kurth S, Stefanucci G, Khosravi E, Verdozzi C, Gross E K U. Phys. Rev. Lett., 2010, 104: art. no. 236801.
[109] Stefanucci G, Kurth S. Phys. Rev. Lett., 2011, 107: art. no. 216401
[1] 杨忠志*. 电负性均衡[J]. 化学进展, 2012, 24(06): 1038-1049.
[2] 苏培峰, 吴玮*. 经典价键理论的从头算计算方法[J]. 化学进展, 2012, 24(06): 1001-1007.
[3] 蒋鸿*. 带隙问题:第一性原理电子能带理论研究现状[J]. 化学进展, 2012, 24(06): 910-927.
[4] 刘文剑. 相对论量子化学新进展*[J]. 化学进展, 2007, 19(06): 833-851.
[5] 李志伟 赵存元 陈六平 . 芳香性团簇的结构和光谱性质的理论研究[J]. 化学进展, 2006, 18(12): 1599-1607.
[6] 张阳,杨基础,于养信,李以圭. 分子模拟在超临界流体领域中的应用[J]. 化学进展, 2005, 17(06): 955-962.
[7] 柴立和. 多尺度科学的研究进展*[J]. 化学进展, 2005, 17(02): 186-191.
[8] 戴瑛,黎乐民. 密度泛函理论处理激发态与多重态结构研究进展[J]. 化学进展, 2001, 13(03): 167-.
[9] 陈凯先,嵇汝运,朱维良,蒋华良,曹阳. 生物大分子体系量子化学计算方法新进展[J]. 化学进展, 1999, 11(04): 367-.