Chain Representations of Open Quantum Systems and Their Numerical Simulation with Time-Adaptive Density Matrix Renormalisation Group Methods

Semiconductors and Semimetals

Volumn 85, Issue , 2011, Pages 115-143

  Chin, Alex W ^a   Huelga, Susana F ^a   Plenio, Martin B ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

Many body simulations; Open quantum systems; Orthogonal polynomials; Photosynthesis; Quantum effects in biology; Time adaptive density matrix renormalisation group

Indexed keywords

EID: 83155193097     PISSN: 00808784     EISSN: None     Source Type: Book Series    
DOI: 10.1016/B978-0-12-391060-8.00004-6     Document Type: Chapter

References (78)

1. Adolphs J., Renger T. Biophys. J. 2006, 91(8):2778.
2. Alvermann A., Fehske H. Phys. Rev. Lett. 2009, 102(15). 150601.
3. Askey R. Orthogonal polynomials and special functions 1975, Society for Industrial Mathematics, Philadelphia.
4. Baker G.A., Graves-Morris P.R. Padé approximants 1996, Cambridge University Press, Cambridge.
5. Barnett S.M., Radmore P.M. Methods in Theoretical Quantum Optics 1997, Oxford University Press, USA.
6. Barthelmann V., Novak E., Ritter K. Adv. Comput. Math. 2000, 12(4):273.
7. Blankenship R.E. Molecular mechanisms of photosynthesis 2002, Wiley-Blackwell, Oxford.
8. Breuer H.P., Laine E.M., Piilo J. Phys. Rev. Lett. 2009, 103(21):210401.
9. Breuer H.P., Petruccione F. The Theory Of Open Quantum Systems 2002, Oxford University Press, USA.
10. Bulla R., Vojta M. Phys. Rev. Lett. 2007, 98(21). 210402.
11. Bulla R., Costi T.A., Pruschke T. Rev. Mod. Phys. 2008, 80(2):395.
12. Bulla R., Lee H.-J., Tong N.-H., Vojta M. Phys. Rev. B 2005, 71(4). 045122.
13. 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(51). 16291.
14. Caram, J. R., and Engel, G. S. (2011). To appear in Faraday Discuss.
15. Caruso F., Chin A.W., Datta A., Huelga S.F., Plenio M.B. J. Chem. Phys. 2009, 131. 105106.
16. Caruso F., Chin A.W., Datta A., Huelga S.F., Plenio M.B. Phys. Rev. A 2010, 81(6). 062346.
17. Chihara T.S. An introduction to orthogonal polynomials 1978, Gordon and Breach, New York; London.
18. Chin A.W., Datta A., Caruso F., Huelga S.F., Plenio M.B. New J. Phys. 2010, 12. 065002.
19. Chin A.W., Rivas A., Huelga S.F., Plenio M.B. J. Math. Phys. 2010, 51. 092109.
20. Chin A.W., Turlakov M. Phys. Rev. B 2006, 73(7). 075311.
21. Collini E., Wong C.Y., Wilk K.E., Curmi P.M.G., Brumer P., Scholes G.D. Nature 2010, 463(7281):644.
22. Daley A.J., Kollath C., Schollwöck U., Vidal G. J. Stat. Mech.: Theor. Exp. 2004, 2004. 04005.
23. Deift P. Orthogonal polynomials and random matrices: a Riemann-Hilbert approach 2000, American Mathematical Society, Providence, R.I.
24. Eisert J., Cramer M., Plenio M.B. Rev. Mod. Phys. 2010, 82(1):277.
25. Engel G.S., Calhoun T.R., Read E.L., Ahn T.K., Mancal T., Cheng Y.C., Blankenship R.E., Fleming G.R. Nature 2007, 446:782.
26. Fassioli F., Nazir A., Olaya-Castro A. J. Phys. Chem. Lett. 2010, 1:2139.
27. Fassioli F., Olaya-Castro A. New J. Phys. 2010, 12. 085006.
28. Garg A., Onuchic J.N., Ambegaokar V. J. Chem. Phys. 1985, 83:4491.
29. Gautschi W. Orthogonal polynomials: computation and approximation 2004, Oxford University Press, USA.
30. Gautschi W. J. Comput. Appl. Math. 2005, 178(1-2):215.
31. Hayes D., Engel G.S. Biophys. J. 2011, 100(8):2043.
32. Hayes D., Panitchayangkoon G., Fransted K.A., Caram J.R., Wen J., Freed K.F., Engel G.S. New J. Phys. 2010, 12. 065042.
33. Hayes D., Wen J., Panitchayangkoon G., Blankenship R.E., Engel G.S. Faraday Discuss. 2011, 150:459.
34. Hughes K.H., Christ C.D., Burghardt I. J. Chem. Phys. 2009, 131. 024109.
35. Hughes K.H., Christ C.D., Burghardt I. J. Chem. Phys. 2009, 131. 124108.
36. Ishizaki A., Calhoun T.R., Schlau-Cohen G.S., Fleming G.R. Phys. Chem. Chem. Phys. 2010, 12(27):7319.
37. Ishizaki A., Fleming G.R. Proc. Natl. Acad. Sci. 2009, 106(41). 17255.
38. Ishizaki A., Fleming G.R. J. Chem. Phys. 2009, 130. 234111.
39. Ismail M. Classical and quantum orthogonal polynomials in one variable 2005, Cambridge University Press, Cambridge.
40. Jang S., Cheng Y.C., Reichman D.R., Eaves J.D. J. Chem. Phys. 2008, 129. 101104.
41. Joos E. Decoherence and the Appearance of a Classical World in Quantum Theory 2003, Springer-Verlag, Berlin; London.
42. Koekoek R., Swarttouw R.F. Arxiv preprint math/9602214 1996.
43. Leggett A.J., Chakravarty S., Dorsey A.T., Fisher M.P.A., Garg A., Zwerger W. Rev. Mod. Phys. 1987, 59(1):1.
44. Martinazzo R., Vacchini B., Hughes K.H., Burghardt I. J. Chem. Phys. 2011, 134(1). 011101.
45. May V., Kühn O. Charge and energy transfer dynamics in molecular systems 2004, Wiley-VCH, Weinheim.
46. Mehta M.L. Random matrices 2004, Elsevier/Academic Press, Amsterdam; London.
47. Mohseni M., Rebentrost P., Lloyd S., Aspuru-Guzik A. J. Chem. Phys. 2008, 129(17). 174106.
48. Müh F., Madjet M.E.A., Adolphs J., Abdurahman A., Rabenstein B., Ishikita H., Knapp E.W., Renger T. Proc. Natl. Acad. Sci. 2007, 104(43). 16862.
49. Mühlbacher L., Rabani E. Phys. Rev. Lett. 2008, 100(17). 176403.
50. Nalbach P., Eckel J., Thorwart M. New J. Phys. 2010, 12. 065043.
51. Nalbach P., Ishizaki A., Fleming G.R., Thorwart M. New J. Phys. 2011, 13. 063040.
52. Nalbach P., Thorwart M. Phys. Rev. B 2010, 81(5). 054308.
53. Nazir A. Phys. Rev. Lett. 2009, 103(14). 146404.
54. Nielsen M.A., Chuang I.L. Quantum Computation and Quantum Information 2011, Cambridge University Press, Cambridge.
55. Nikiforov A.F., Suslov S.K., Uvarov V.B. Classical orthogonal polynomials of a discrete variable 1991, Springer-Verlag, Berlin.
56. Olaya-Castro A., Lee C.F., Olsen F.F., Johnson N.F. Phys. Rev. B 2008, 78(8). 085115.
57. Olbrich C., Strmpfer J., Schulten K., Kleinekathöfer U. J. Phys. Chem. B. 2010, 115(4):758.
58. Panitchayangkoon G., Hayes D., Fransted K.A., Caram J.R., Harel E., Wen J., Blankenship R.E., Engel G.S. Proc. Natl Acad. Sci. 2010, 107(29). 12766.
59. Plenio M.B., Huelga S.F. New J. Phys. 2008, 10. 113019.
60. Prior J., Chin A.W., Huelga S.F., Plenio M.B. Phys. Rev. Lett. 2010, 105(5). 050404.
61. Rebentrost P., Mohseni M., Kassal I., Lloyd S., Aspuru-Guzik A. New J. Phys. 2009, 11. 033003.
62. Rivas Á, Huelga S.F., Plenio M.B. Phys. Rev. Lett. 2010, 105(5). 50403.
63. Roden J., Eisfeld A., Wolff W., Strunz W.T. Phys. Rev. Lett. 2009, 103(5). 58301.
64. Sarovar M., Ishizaki A., Fleming G.R., Whaley K.B. Nat. Phys. 2010, 6(6):462.
65. Schmidt am Busch M., Müh F., El-Amine Madjet M., Renger T. J. Phys. Chem. Lett. 2010, 2:93.
66. Schollwöck U. Rev. Mod. Phys. 2005, 77(1):259.
67. Szegö G. Orthogonal polynomials 1967, American Mathematical Society, Providence, R.I.
68. Thorwart M., Eckel J., Reina J.H., Nalbach P., Weiss S. Chem. Phys. Lett. 2009, 478(4-6):234.
69. Van Amerongen H., Valkunas L., Van Grondelle R. Photosynthetic excitons 2000, World Scientific, Singapore.
70. Vidal G. Phys. Rev. Lett. 2004, 93(4). 040502.
71. Vojta M., Tong N.H., Bulla R. Phys. Rev. Lett. 2005, 94(7). 70604.
72. Walls D.F., Milburn G.J. Quantum optics 2008, Springer Verlag, Berlin.
73. Weiss U. Quantum Dissipative Systems 1993, World Scientific, Singapore.
74. White S.R., Feiguin A.E. Phys. Rev. Lett. 2004, 93(7). 76401.
75. Winter A., Rieger H., Vojta M., Bulla R. Phys. Rev. Lett. 2009, 102(3). 030601.
76. Xiu, D. (2003)."The wiener-askey polynomial chaos for stochastic differential equations". Technical report DTIC Document.
77. Zhu J., Kais S., Rebentrost P., Aspuru-Guzik A. J. Phys. Chem. B 2011, 115(6):1531.
78. Zwolak M., Vidal G. Phys. Rev. Lett. 2004, 93(20). 207205.