Master equation approach to line shape in dissipative systems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 2, 2009, Pages

  Uchiyama, Chikako ^a   Aihara, Masaki ^b   Saeki, Mizuhiko ^c,d   Miyashita, Seiji ^c,d  

^a UNIVERSITY OF YAMANASHI   (Japan)

^b NARA INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

^c UNIVERSITY OF TOKYO   (Japan)

^d JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

A-THERMAL; COMPACT FORMULAS; COMPLEX SUSCEPTIBILITY; CUMULANTS; DENSITY OPERATORS; DISSIPATIVE EFFECTS; DISSIPATIVE SYSTEMS; EQUATION OF MOTION; FREQUENCY SHIFT; LINE SHAPE; MAGNETIC RESPONSE; MASTER EQUATIONS; NON-MARKOVIAN DYNAMICS; RESPONSE FUNCTIONS; SECOND ORDERS; SPATIAL ORIENTATIONS; SPECTRAL FUNCTION; SPIN SYSTEMS; STATIC FIELDS; THERMAL BATH; THERMAL ENVIRONMENT; THREE-SPIN SYSTEM; TIME EVOLUTIONS; TWO-SPIN SYSTEMS;

EQUATIONS OF MOTION; FREQUENCY SHIFT KEYING; MATHEMATICAL OPERATORS; SPECTROSCOPY;

SPIN DYNAMICS;

EID: 70349243204     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.021128     Document Type: Article

References (67)

1. I. Chiorescu, W. Wernsdorfer, A. Muller, H. Bogge, and B. Barbara, Phys. Rev. Lett. 84, 3454 (2000). 10.1103/PhysRevLett.84.3454
2. L. Thomas, Nature (London) 383, 145 (1996). 10.1038/383145a0 (Pubitemid 26303971)
3. S. Bertaina, Nature (London) 453, 203 (2008). 10.1038/nature06962 (Pubitemid 351667986)
4. D. Gatteschi, A. Caneschi, L. Pardi, and R. Sessoli, Science 265, 1054 (1994). 10.1126/science.265.5175.1054
5. H. Hachisuka, K. Awaga, T. Yokoyama, T. Kubo, T. Goto, and H. Nojiri, Phys. Rev. B 70, 104427 (2004). 10.1103/PhysRevB.70.104427
6. Y. Furukawa, K. Kumagai, A. Lascialfari, S. Aldrovandi, F. Borsa, R. Sessoli, and D. Gatteschi, Phys. Rev. B 64, 094439 (2001). 10.1103/PhysRevB.64. 094439
7. M. Ueda, S. Maegawa, and S. Kitagawa, Phys. Rev. B 66, 073309 (2002). 10.1103/PhysRevB.66.073309
8. T. Kubo, T. Goto, T. Koshiba, K. Takeda, and K. Awaga, Phys. Rev. B 65, 224425 (2002). 10.1103/PhysRevB.65.224425
9. T. Sakon, Physica B 346, 206 (2004). 10.1016/j.physb.2004.01.051
10. J. H. Van Vleck, Phys. Rev. 74, 1168 (1948). 10.1103/PhysRev.74.1168
11. R. Kubo and K. Tomita, J. Phys. Soc. Jpn. 9, 888 (1954). 10.1143/JPSJ.9.888
12. M. Suzuki and R. Kubo, J. Phys. Soc. Jpn. 24, 51 (1968). 10.1143/JPSJ.24.51
13. S. Miyashita, T. Yoshino, and A. Ogasahara, J. Phys. Soc. Jpn. 68, 655 (1999). 10.1143/JPSJ.68.655
14. A. Ogasahara and S. Miyshita, J. Phys. Soc. Jpn. 69, 4043 (2000). 10.1143/JPSJ.69.4043 (Pubitemid 33232185)
15. S. Miyashita and A. Ogasahara, J. Phys. Soc. Jpn. 72, 2350 (2003). 10.1143/JPSJ.72.2350
16. A. Ogasahara and S. Miyashita, J. Phys. Soc. Jpn. Suppl. B 72, 44 (2003).
17. I. Affleck and M. Oshikawa, Phys. Rev. B 60, 1038 (1999). 10.1103/PhysRevB.60.1038
18. M. Oshikawa and I. Affleck, Phys. Rev. Lett. 82, 5136 (1999). 10.1103/PhysRevLett.82.5136
19. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957) 10.1143/JPSJ.12.570
20. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer-Verlag, New York, 1985).
21. S. Nakajima, Prog. Theor. Phys. 20, 948 (1958). 10.1143/PTP.20.948
22. R. Zwanzig, J. Chem. Phys. 33, 1338 (1960). 10.1063/1.1731409
23. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973), Sec. 6.6.
24. A. Abragam, Principles of Nuclear Magnetism (Oxford Press, London, 1961) and cited therein.
25. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1992), Sec. AV-3, c.
26. Y. Hamano and F. Shibata, J. Phys. C 17, 4843 (1984). 10.1088/0022-3719/17/27/014
27. F. Shibata and M. Asou, J. Phys. Soc. Jpn. 49, 1234 (1980) 10.1143/JPSJ.49.1234
28. M. Asou and F. Shibata, J. Phys. Soc. Jpn. 50, 1846 (1981) 10.1143/JPSJ.50.1846
29. M. Asou and F. Shibata, J. Phys. Soc. Jpn. 50, 2481 (1981). 10.1143/JPSJ.50.2481
30. L. Onsager, Phys. Rev. 38, 2265 (1931). 10.1103/PhysRev.38.2265
31. M. Lax, Phys. Rev. 172, 350 (1968). 10.1103/PhysRev.172.350
32. R. Graham, F. Haake, H. Haken, and W. Weidlich, Z. Phys. 213, 21 (1968). 10.1007/BF01380024
33. F. Haake, Phys. Rev. A 3, 1723 (1971). 10.1103/PhysRevA.3.1723
34. M. Sassetti and U. Weiss, Phys. Rev. A 41, 5383 (1990). 10.1103/PhysRevA.41.5383
35. U. Weiss, Quantum Dissipative Systems, 2nd ed. (World Scientific, Singapore, 1999).
36. H.-P. Breuer, B. Kappler, and F. Petruccione, Ann. Phys. 291, 36 (2001) 10.1006/aphy.2001.6152
37. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2002).
38. Y. Tanimura, J. Phys. Soc. Jpn. 75, 082001 (2006) and cited therein. 10.1143/JPSJ.75.082001
39. M. Saeki, Physica A 387, 1827 (2008) and cited therein. 10.1016/j.physa.2007.11.016
40. K. Nagata and Y. Tazuke, J. Phys. Soc. Jpn. 32, 337 (1972). 10.1143/JPSJ.32.337
41. E. C. G. Sudarshan, P. M. Mathews, and J. Rau, Phys. Rev. 121, 920 (1961) 10.1103/PhysRev.121.920
42. A. Kossakowski, Rep. Math. Phys. 3, 247 (1972) 10.1016/0034-4877(72) 90010-9
43. A. Kossakowski, Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. Phys. 20, 1021 (1972)
44. A. Kossakowski, Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. Phys. 21, 649 (1973)
45. G. Lindblad, Commun. Math. Phys. 48, 119 (1976) 10.1007/BF01608499
46. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976) 10.1063/1.522979
47. V. Gorini, A. Frigerio, M. Verri, A. Kossakowski, and E. C. G. Sudarshan, Rep. Math. Phys. 13, 149 (1978). 10.1016/0034-4877(78)90050-2
48. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994). 10.1103/PhysRevLett.73. 1060
49. A. Suárez, R. Silbey, and I. Oppenheim, J. Chem. Phys. 97, 5101 (1992). 10.1063/1.463831
50. P. Gaspard and M. Nagaoka, J. Chem. Phys. 111, 5668 (1999). 10.1063/1.479867
51. T. Mori and S. Miyashita, J. Phys. Soc. Jpn. 77, 124005 (2008). 10.1143/JPSJ.77.124005
52. A. J. Leggett, Rev. Mod. Phys. 59, 1 (1987). 10.1103/RevModPhys.59.1
53. U. Weiss, Quantum Dissipative Systems, 1st ed. (World Scientific, Singapore, 1993)
54. Quantum Dissipative Systems, 2nd ed. (World Scientific, Singapore, 1999).
55. A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983). 10.1016/0003-4916(83)90202-6
56. N. V. Prokof'ev and P. C. E. Stamp, Rep. Prog. Phys. 63, 669 (2000) 10.1088/0034-4885/63/4/204
57. N. V. Prokof'ev and P. C. E. Stamp, J. Phys. Chem. Lett. 5, L663 (1993)
58. P. C. E. Stamp, Physica B 197, 133 (1994) 10.1016/0921-4526(94)90207-0
59. N. V. Prokof'ev and P. C. E. Stamp, J. Low Temp. Phys. 104, 143 (1996). 10.1007/BF00754094
60. A. E. Allahverdyan, R. S. Gracia, and Th. M. Nieuwenhuizen, Phys. Rev. E 71, 046106 (2005). 10.1103/PhysRevE.71.046106
61. N. Hashitsume, F. Shibata, and M. Shingu, J. Stat. Phys. 17, 155 (1977). 10.1007/BF01040099
62. F. Shibata and C. Uchiyama, J. Phys. Soc. Jpn. 62, 381 (1993). 10.1143/JPSJ.62.381
63. K.-Y. Choi, Y. H. Matsuda, H. Nojiri, U. Kortz, F. Hussain, A. C. Stowe, C. Ramsey, and N. S. Dalal, Phys. Rev. Lett. 96, 107202 (2006). 10.1103/PhysRevLett.96.107202
64. C. Uchiyama and F. Shibata, Phys. Rev. E 60, 2636 (1999). 10.1103/PhysRevE.60.2636
65. C. Uchiyama and F. Shibata, Phys. Lett. A 267, 7 (2000). 10.1016/S0375-9601(00)00064-5
66. E. B. Davies, Quantum Theory of Open Systems (Academic Press, London, 1976).
67. The procedure of Born-Markovian approximation can also be understood by using the interaction picture and assuming that the time evolution of ρ Aν (t-s) can be approximated with ρ Aν (t) because of the short correlation time of the bath.