Continuous-time quantum walks: Models for coherent transport on complex networks

Physics Reports

Volumn 502, Issue 2-3, 2011, Pages 37-87

  Mülken, Oliver ^a   Blumen, Alexander ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Coherent and incoherent dynamics; Complex networks; Excitons; Quantum transport

Indexed keywords

EID: 79954686949     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2011.01.002     Document Type: Review

References (132)

1. Bouchaud J.-P., Georges A. Phys. Rep. 1990, 195:127.
2. Albert R., Barabási A.-L. Rev. Modern Phys. 2002, 74:47.
3. Dorogovtsev S.N., Mendes J.F.F. Adv. Phys. 2002, 51:1079.
4. Kempe J. Contemp. Phys. 2003, 44:307.
5. van Kampen N. Stochastic Processes in Physics and Chemistry 1990, North-Holland, Amsterdam.
6. Weiss G.H. Aspects and Applications of the Random Walk 1994, North-Holland, Amsterdam.
7. Ziman J.M. Principles of the Theory of Solids 1972, Cambridge University Press, Cambridge, England.
8. Kenkre V.M., Reineker P. Exciton Dynamics in Molecular Crystals and Aggregates 1982, Springer, Berlin.
9. Ashcroft N.W., Mermin N.D. Solid State Physics 1976, Saunders College Publishing, Philadelphia.
10. Kittel C. Introduction to Solid State Physics 1986, Wiley, New York.
11. Anderson P.W. Phys. Rev. 1958, 109:1492.
12. Mcquarrie D.A. Quantum Chemistry 1983, Oxford University Press, Oxford.
13. Doi M., Edwards S.F. The Theory of Polymer Dynamics 1998, Oxford University Press, Oxford.
14. Scher H., Lax M. Phys. Rev. B 1973, 7:4491.
15. Scher H., Montroll E.W. Phys. Rev. B 1975, 12:2455.
16. Alexander S., Orbach R. J. Phys. (Paris) Lett. 1982, 43:L625.
17. Klafter J., Blumen A. J. Chem. Phys. 1984, 80:875.
18. Even U., Rademann K., Jortner J., Manor N., Reisfeld R. Phys. Rev. Lett. 1984, 52:2164.
19. Klafter J., Blumen A., Shlesinger M.F. Phys. Rev. A 1987, 35:3081.
20. Zumofen G., Blumen A., Klafter J., Shlesinger M. J. Stat. Phys. 1989, 54:1519.
21. Farhi E., Gutmann S. Phys. Rev. A 1998, 58:915.
22. Aharonov Y., Davidovich L., Zagury N. Phys. Rev. A 1993, 48:1687.
23. Mülken O., Blumen A. Phys. Rev. E 2005, 71:016101.
24. Bose S. Phys. Rev. Lett. 2003, 91:207901.
25. Strauch F.W. Phys. Rev. A 2006, 74:030301(R).
26. Nielsen M.A., Chuang I.L. Quantum Computation and Quantum Information 2000, Cambridge University Press, Cambridge, England.
27. Shor P.W. 35th IEEE Symposium on Foundations of Computer Science 1994, IEEE, Los Alamos, p. 124.
28. Grover L.K. Phys. Rev. Lett. 1997, 79(2):325.
29. Childs A.M., Goldstone J. Phys. Rev. A 2004, 70:022314.
30. Agliari E., Blumen A., Mülken O. Phys. Rev. A 2010, 82:012305.
31. Feynman R.P. Internat. J. Theoret. Phys. 1982, 21:467.
32. Meyer D.A. J. Stat. Phys. 1996, 85:551.
33. Christandl M., Datta N., Ekert A., Landahl A.J. Phys. Rev. Lett. 2004, 92:187902.
34. Kottos T., Smilansky U. Phys. Rev. Lett. 1997, 79:4794.
35. Schanz H., Smilansky U. Phys. Rev. Lett. 2000, 84:1427.
36. Kottos T., Smilansky U. Phys. Rev. Lett. 2000, 85:968.
37. Kottos T., Schanz H. Phys. Rev. Lett. 2003, 90:234101.
38. Smilansky U. J. Phys. A 2007, 40:F621.
39. Sakurai J. Modern Quantum Mechanics 1994, Addison-Wesley, Redwood City, CA. 2nd ed,.
40. Kinzel W. Phys. Bl. 1995, 51:1190.
41. Grossmann F., Rost J.-M., Schleich W.P. J. Phys. A 1997, 30:L277.
42. Berry M.V. J. Phys. A 1996, 29:6617.
43. Bloch I. Nat. Phys. 2005, 1:23.
44. Sanders B.C., Bartlett S.D., Fregenna B., Knight P.L. Phys. Rev. A 2003, 67:042305.
45. CÔté R., Russel A., Eyler E.E., Gould P.L. New J. Phys. 2006, 8:156.
46. Dür W., Raussendorf R., Kendon V.M., Briegel H.-J. Phys. Rev. A 2002, 66:052319.
47. Knight P.L., Roldán E., Sipe J.E. Opt. Commun. 2003, 227:147.
48. Zhang P., Ren X.-F., Zou X.-B., Liu B.-H., Huang Y.-F., Guo G.-C. Phys. Rev. A 2007, 75:052310.
49. Perets H.B., Lahini Y., Pozzi F., Sorel M., Morandotti R., Silberberg Y. Phys. Rev. Lett. 2008, 100:170506.
50. Mülken O., Blumen A., Amthor T., Giese C., Reetz-Lamour M., Weidemüller M. Phys. Rev. Lett. 2007, 99:090601.
51. D. Burgarth, Quantum state transfer with spin chains, Ph.D. Thesis, University College London, 2006.
52. Bose S. Contemp. Phys. 2007, 48:13.
53. Anderson W.R., Veale J.R., Gallagher T.F. Phys. Rev. Lett. 1998, 80:249.
54. Mourachko I., Comparat C., de Tomasi F., Fioretti A., Nosbaum P., Akulin V., Pillet P. Phys. Rev. Lett. 1998, 80:253.
55. Westermann S., Amthor T., de Oliveira A.L., Deiglmayr J., Reetz-Lamour M., Weidemüller M. Eur. Phys. J. D 2006, 40:37.
56. Engel G.S., Calhoun T.R., Read R.L., Ahn T.-K., Manal T., Cheng Y.-C., Blankenship R.E., Fleming G.R. Nature 2007, 446:782.
57. Collini E., Wong C.Y., Wilk K.E., Curmi P.M.G., Brumer P., Scholes G.D. Nature 2010, 463:644.
58. Heijs D.-J., Malyshev V.A., Knoester J. J. Chem. Phys. 2004, 121:4884.
59. Vlaming S.M., Heijs D.J., Knoester J. J. Lumin. 2005, 111:349.
60. Blumen A., Volta A., Jurjiu A., Koslowski T. J. Lumin. 2005, 111:327.
61. Shortreed M.R., Swallen S.F., Shi Z.-Y., Tan W., Xu Z., Devadoss C., Moore J.S., Kopelman R. J. Phys. Chem. B 1997, 101:6318.
62. Varnavski O., Samuel I.D.W., Palsson L.-O., Beavington R., Burn P.L., Goodson T. J. Chem. Phys. 2002, 116:8893.
63. Varnavski O.P., Ostrowski J.C., Sukhomlinova L., Twieg R.J., Bazan G.C., Goodson T. J. Am. Chem. Soc. 2002, 124:1736.
64. Fleming G.R., Scholes G.D. Nature 2004, 431:256.
65. Cheng Y.C., Silbey R.J. Phys. Rev. Lett. 2006, 96:028103.
66. Mohseni M., Rebentrost P., Lloyd S., Aspuru-Guzik A. J. Chem. Phys. 2008, 129:174106.
67. Plenio M.B., Huelga S.F. New J. Phys. 2008, 10:113019.
68. Caruso F., Chin A.W., Datta A., Huelga S.F., Plenio M.B. J. Chem. Phys. 2009, 131:105106.
69. Olaya-Castro A., Lee C.F., Olsen F.F., Johnson N.F. Phys. Rev. B 2008, 78:085115.
70. Breuer H.-P., Petruccione F. The Theory of Open Quantum Systems 2006, Oxford University Press, Oxford, England.
71. Aharonov D., Ambainis A., Kempe J., Vazirani U. Proceedings of ACM Symposium on Theory of Computation 2001, ACM Press, New York, p. 50.
72. Mülken O., Volta A., Blumen A. Phys. Rev. A 2005, 72:042334.
73. Mülken O., Blumen A. Phys. Rev. E 2005, 71:036128.
74. Mülken O., Blumen A. Phys. Rev. E 2006, 73:066117.
75. O. Mülken, Preprint (2007) arxiv:0710.3453.
76. Gradshteyn I.S., Ryzhik I.M. Table of Integrals Series and Products 1980, Academic Press.
77. Alexander S., Bernasconi J., Schneider W.R., Orbach R. Rev. Modern Phys. 1981, 53:175.
78. Salimi S. Quantum Inf. Process. 2009, 9:75.
79. Encyclopedic Dictionary of Mathematics 1987, MIT-Press, Cambridge, MA. K. Ito (Ed.).
80. Volta A., Mülken O., Blumen A. J. Phys. A 2006, 39:14997.
81. Xu X.P. J. Phys. A 2009, 42:115205.
82. Salimi S. Ann. Phys. 2009, 324:1185.
83. Mülken O., Bierbaum V., Blumen A. J. Chem. Phys. 2006, 124:124905.
84. Cai C., Chen Z.Y. Macromolecules 1997, 30:5104.
85. Iwanow R., May-Arrioja D.A., Christodoulides D.N., Stegeman G.I., Min Y., Sohler W. Phys. Rev. Lett. 2005, 95:053902.
86. Bar-Haim A., Klafter J., Kopelman R. J. Am. Chem. Soc. 1997, 119:6197.
87. Rana D., Gangopadhyay G. J. Chem. Phys. 2003, 118:434.
88. Poliakov E.Y., Chernyak V., Tretiak S., Mukamel S. J. Chem. Phys. 1999, 110:8161.
89. Blumen A., Bierbaum V., Mülken O. Physica A 2006, 371:10.
90. Childs A.M., Farhi E., Gutmann S. Quantum Inf. Process. 2002, 1:35.
91. Agliari E., Blumen A., Mülken O. J. Phys. A 2008, 41:445301.
92. Cosenza M.G., Kapral R. Phys. Rev. A 1992, 46:1850.
93. Blumen A., Jurjiu A. J. Chem. Phys. 2002, 116:2636.
94. Mülken O., Pernice V., Blumen A. Phys. Rev. E 2007, 76:051125.
95. Jespersen S., Sokolov I.M., Blumen A. Phys. Rev. E 2000, 62:4405.
96. Heller E.J. Phys. Rev. A 1987, 35:1360.
97. Xu X.P., Liu F. Phys. Lett. A 2008, 372:6727.
98. Xu X.P., Liu F. New J. Phys. 2008, 10:123012.
99. Xu X.P., Li W., Liu F. Phys. Rev. E 2008, 78:052103.
100. Mülken O., Pernice V., Blumen A. Phys. Rev. E 2008, 77:021117.
101. Handbook of Mathematical Functions 1972, Dover, New York. M. Abramowitz, I.A. Stegun (Eds.).
102. Bender C.M., Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers 1978, McGraw-Hill Inc.
103. Xu X.P. Phys. Rev. E 2008, 77:061127.
104. Mülken O., Bierbaum V., Blumen A. Phys. Rev. E 2007, 75:031121.
105. Yin Y., Katsanos D.E., Evangelou S.N. Phys. Rev. A 2008, 77:022302.
106. Mülken O., Pernice V., Blumen A. Phys. Rev. E 2008, 78:021115.
107. Agliari E., Mülken O., Blumen A. Internat. J. Bifur. Chaos 2010, 20:271.
108. Mülken O., Blumen A. Physica E 2010, 42:576.
109. Sternheim M.M., Walker J.F. Phys. Rev. C 1972, 6:114.
110. Parris P.E. Phys. Rev. B 1989, 40:4928.
111. Xu X.P. Phys. Rev. E 2009, 79:0n11117.
112. Volta A. J. Phys. A 2009, 42:225003.
113. Blumen A., von Ferber C., Jurjiu A., Koslowski T. Macromolecules 2004, 37:638.
114. Schleich W.P. Quantum Optics in Phase Space 2001, Wiley-VCH, Berlin.
115. Wigner E.P. Phys. Rev. 1932, 40:749.
116. Hillery M., O'Connell R.F., Scully M.O., Wigner E.P. Phys. Rep. 1984, 106:121.
117. Wootters W.K. Ann. Phys. 1987, 176:1.
118. Cohendet O., Combe P., Sirugeu M., Sirugue-Collin M. J. Phys. A 1988, 21:2875.
119. Leonhardt U. Phys. Rev. Lett. 1995, 74:4101.
120. Leonhardt U. Phys. Rev. A 1996, 53:2998.
121. Mülken O., Blumen A. Phys. Rev. A 2006, 73:012105.
122. Xu X.P., Liu F. Phys. Rev. A 2008, 77:062318.
123. Caldeira A.O., Legget A.J. Ann. Phys. 1983, 149:374.
124. Caldeira A.O., Legget A.J. Ann. Phys. 1984, 153:445(E).
125. Gurvitz S.A., Fedichkin L., Mozyrsky D., Berman G.P. Phys. Rev. Lett. 2003, 91:066801.
126. Solenov D., Fedichkin L. Phys. Rev. A 2006, 73:012308.
127. Solenov D., Fedichkin L. Phys. Rev. A 2006, 73:012313.
128. Fedichkin L., Solenov D., Tamon C. Quantum. Inf. Process. 2006, 6:263.
129. Salimi S., Radgohar R. J. Phys. A 2009, 42:475302.
130. Mülken O., Mühlbacher L., Schmid T., Blumen A. Phys. Rev. E 2010, 81:041114.
131. Mühlbacher L., Ankerhold J., Escher C. J. Chem. Phys. 2004, 121:12696.
132. Mühlbacher L., Ankerhold J. J. Chem. Phys. 2005, 122:184715.