Decoherence and thermalization of quantum spin systems

Journal of Computational and Theoretical Nanoscience

Volumn 8, Issue 6, 2011, Pages 889-911

  Yuan, Shengjun ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Canonical ensemble; Decoherence; Quantum statistical mechanics; Second law of thermodynamics; Time dependent schr dinger equation

Indexed keywords

CANONICAL ENSEMBLE; DECOHERENCE; DECOHERENCE PROCESS; DIAGONAL ELEMENTS; DINGER EQUATION; EIGENENERGIES; EQUILIBRIUM STATE; INITIAL STATE; INTEGRALS OF MOTION; MAXIMUM ENTROPY; NUMERICAL RESULTS; QUANTUM DYNAMICS; QUANTUM MECHANICS; QUANTUM SPIN SYSTEMS; QUANTUM STATISTICAL MECHANICS; QUANTUM SYSTEM; REDUCED-DENSITY MATRIX; SECOND LAW OF THERMODYNAMICS; SPIN BATH; SPIN SYSTEMS; SPIN-SPIN COUPLINGS; SUB-SPACES; THERMALIZATION; TIME AVERAGING; TIME-DEPENDENT; WHOLE SYSTEMS;

QUANTUM ELECTRONICS; QUANTUM OPTICS; SPIN DYNAMICS; STATISTICAL MECHANICS;

THERMODYNAMICS;

EID: 79955432057     PISSN: 15461955     EISSN: None     Source Type: Journal    
DOI: 10.1166/jctn.2011.1772     Document Type: Review

References (97)

1. R. V. Jensen and R. Shankar, Phys. Rev. Lett. 54, 1879 (1985).
2. H. D. Zeh, Foundation of Physics 1, 69 (1970).
3. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory, Springer, Berlin (1996).
4. W. H. Zurek, Phys. Rev. D 24, 1516 (1981).
5. W. H. Zurek, Phys. Rev. D 26, 1862 (1982).
6. W. H. Zurek, Physics Today 44, 36 (1991).
7. W. H. Zurek, Phil. Trans. R. Soc. Lond. A 356, 1793 (1998).
8. W. H. Zurek, Los Alamos Sci. 27, 86 (2002).
9. W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).
10. W. H. Zurek, Nat. Phys. 5, 181 (2009).
11. J.-P. Paz and W. H. Zurek, Phys. Rev. Lett. 82, 5181 (1999).
12. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000).
13. B. E. Kane, Nature 393, 133 (1998).
14. M. N. Leuenberger and D. Loss, Nature 410, 789 (2001).
15. B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, Nat. Phys. 3, 192 (2007).
16. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton (1955).
17. R. P. Feynman and F. L. Vernon, Ann. Phys. (N.Y.) 24, 118 (1963).
18. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
19. N. V. Prokof'ev and P. C. E. Stamp, Rep. Prog. Phys. 63, 669 (2000).
20. V. V. Dobrovitski, H. A. De Raedt, M. I. Katsnelson, and B. N. Harmon, Phys. Rev. Lett. 90, 210401 (2003).
21. J. Lages, V. V. Dobrovitski, M. I. Katsnelson, and B. N. Harmon, Phys. Rev. E 72, 026225 (2005).
22. A. Melikidze, V. V. Dobrovitski, H. A. De Raedt, M. I. Katsnelson, and B. N. Harmon, Phys. Rev B 70, 014435 (2004).
23. S. Yuan, M. I. Katsnelson, and H. De Raedt, JETP Lett. 84, 99 (2006).
24. S. Yuan, M. I. Katsnelson, and H. De Raedt, Phys. Rev. A 75, 052109 (2007).
25. S. Yuan, M. I. Katsnelson, and H. De Raedt, Phys. Rev. B 77, 184301 (2008).
26. S. Yuan, M. I. Katsnelson, and H. De Raedt, J. Phys. Soc. Jpn. 78, 094003 (2009).
27. J. van Wezel, J. van den Brink, and J. Zaanen, Phys. Rev. Lett. 94, 230401 (2005).
28. X. Z. Yuan, H.-S. Goan, and K. D. Zhu, Phys. Rev. B 75, 045331 (2007).
29. X. Z. Yuan and K. D. Zhu, Europhys. Lett. 69, 868 (2005).
30. Y. Gao and S. J. Xiong, Phys. Rev. A 71, 034102 (2005).
31. W. Zhang, V. V. Dobrovitski, K. A. Al-Hassanieh, E. Dagotto, and B. N. Harmon, Phys. Rev. B 74, 205313 (2006).
32. W. Zhang, N. Konstantinidis, K. A. Al-Hassanieh, and V. V. Dobrovitski, J. Phys. Cond. Matter 19, 083202 (2007).
33. C. M. Dawson, A. P. Hines, R. H. McKenzie, and G. J. Milburn, Phys. Rev. A 71, 052321 (2005).
34. D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, and R. Fazio, Phys. Rev. A 75, 032333 (2007).
35. L. Tessieri and J. Wilkie, J. Phys. A, Math. Gen. 36, 12305 (2003).
36. S. Camalet and R. Chitra, Phys. Rev. B 75, 094434 (2007).
37. D. D. B. Rao, V. Ravishankar, and V. Subrahmanyam, Phys. Rev. A 75, 052338 (2007).
38. A. Relano, J. Dukelsky, and R. A. Molina, Phys. Rev. E 76, 046223 (2007).
39. V. V. Dobrovitski, M. I. Katsnelson, and B. N. Harmon, Phys. Rev. Lett. 84, 3458 (2000).
40. S. O. Skrovseth, Europhys. Lett. 76, 1179 (2006).
41. G.-F. Zhang, J.-Q. Liang, G.-E. Zhang, and Q.-W. Yan, Eur. Phys. J. D 32, 409 (2005).
42. Y. Hamdouni, M. Fannes, and F. Petruccione, Phys. Rev. B 73, 245323 (2006).
43. K. Saito, S. Takasue, and S. Miyashita, Phys. Rev. Lett. 65, 1243 (1996).
44. P. Bocchieri and A. Loinger, Phys. Rev. 114, 948 (1959).
45. R. V. Jensen and R. Shankar, Phys. Rev. Lett. 54, 1879 (1985).
46. H. Tasaki, Phys. Rev. Lett. 80, 1373 (1998).
47. S. Popescu, A. J. Short, and A. Winter, Nat. Phys. 2, 754 (2006).
48. M. Rigol, V. Dunjko, and M. Olshanii, Nature 452, 854 (2008).
49. S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zangh, Phys. Rev. Lett. 96, 050403 (2006).
50. P. Reimann, Phys. Rev. Lett. 99, 160404 (2007).
51. P. Reimann, J. Stat. Phys. 132, 921 (2008).
52. J. Gemmer and M. Michel, Europhys. Lett. 73, 1 (2006).
53. J. Gemmer and M. Michel, Eur. Phys. J. B 53, 517 (2006).
54. M. A. Cazalilla, Phys. Rev. Lett. 97, 156403 (2006).
55. M. Rigol, A. Muramatsu, and M. Olshanii, Phys. Rev. A 74, 053616 (2006).
56. M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007).
57. M. Eckstein and M. Kollar, Phys. Rev. Lett. 100, 120404 (2008).
58. M. Cramer, A. Flesch, I. P. McCulloch, U. Schollwock, and J. Eisen, Phys. Rev. Lett. 101, 063001 (2008).
59. M. Cramer, C. M. Dawson, J. Eisert, and T. J. Osborne, Phys. Rev. Lett. 100, 030602 (2008).
60. A. Flesch, M. Cramer, I. P. McCulloch, U. Schollwock, and J. Eisert, Phys. Rev. A 78, 033608 (2008).
61. M. Esposito and P. Gaspard, Phys. Rev. E 68, 066113 (2003).
62. M. Merkli and I. M. Sigal, Phys. Rev. Lett. 98, 130401 (2007).
63. G. Benenti, G. Casati, and D. L. Shepelyansky, Eur. Phys. J. D 17, 265 (2001).
64. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York (1975).
65. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton (1955).
66. L. E. Ballentine, Quantum Mechanics, A Modern Development, World Scientific, Singapore (2003).
67. M. Znidaric and T. Prosen, J. Phys. A: Math. Gen. 36, 2463 (2003).
68. T. Prosen, T. H. Seligman, and M. Znidaric, Prog. Theor. Phys. Suppl. 150, 200 (2003).
69. F. M. Cucchietti, D. A. R. Dalvit, J. P. Paz, and W. H. Zurek, Phys. Rev. Lett. 91, 210403 (2003).
70. H. Fujisaki, T. Miyadera, and A. Tanaka, Phys. Rev. E 67, 066201 (2003).
71. T. Gorin, T. Prosen, T. H. Seligman, and M. Znidaric, Physics Reports, 435, 33 (2006).
72. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008).
73. K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986).
74. M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond, World Scientific, Singapore (1987).
75. H. Tal-Ezer and R. Kosloff, J. Chem. Phys. 81, 3967 (1984).
76. C. Leforestier, R. H. Bisseling, C. Cerjan, M. D. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, J. Comp. Phys. 94, 59 (1991).
77. T. Iitaka, S. Nomura, H. Hirayama, X. Zhao, Y. Aoyagi, and T. Sugano, Phys. Rev. E 56, 1222 (1997).
78. V. V. Dobrovitski and H. De Raedt, Phys. Rev. E 67, 056702 (2003).
79. H. F. Trotter, Pmc. Am. Math. Soc. 10, 545 (1959).
80. M. Suzuki, S. Miyashita, and A. Kuroda, Prog. Theor. Phys. 58, 1377 (1977).
81. M. Suzuki, J. Math. Phys. 26, 601 (1985).
82. M. Suzuki, J. Math. Phys. 32, 400 (1991).
83. H. De Raedt and B. De Raedt, Phys. Rev. A 28, 3575 (1983).
84. H. De Raedt, Comp. Phys. Rep. 7, 1 (1987).
85. H. De Raedt and P. de Vries, Z. Phys. B 77, 243 (1989).
86. P. de Vries and H. De Raedt, Phys. Rev. B 47, 7929 (1993).
87. K. Michielsen, H. De Raedt, J. Przeslawski, and N. García, Phys. Rep. 304, 89 (1998).
88. H. De Raedt, A. H. Hams, K. Michielsen, and K. De Raedt, Comp. Phys. Comm. 132, 1 (2000).
89. H. De Raedt and K. Michielsen, Computational methods for simulating quantum computers, Handbook of Theoretical and Computational Nanotechnology, Quantum and Molecular Computing, Quantum Simulations, edited by M. Rieth and W. Schommers, American Scientific Publisher, Los Angeles (2006), Vol. 3, Chap. 1, pp. 2-48.
90. M. Krech, A. Bunker, and D. P. Landau, Comp. Phys. Comm. 111,1 (1998).
91. S. Yuan, H. De Raedt, and S. Miyashita, J. Phys. Soc. Jpn. 75, 084703 (2006).
92. S. Yuan, H. De Raedt, and S. Miyashita, Phys. Rev. B 75, 184305 (2007).
93. A. H. Hams and H. De Raedt, Phys. Rev. E 62, 4365 (2000).
94. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
95. S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997).
96. A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford (1961).
97. E. T. Jaynes, Phys. Rev. 106, 620 (1957).