Quantum dynamics under time-dependent external fields

Journal of Computational and Theoretical Nanoscience

Volumn 8, Issue 6, 2011, Pages 919-936

  Miyashita, Seiji ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

Dzyaloshinsky moriya interaction; ESR; Floquet theorem; Jayens cummings model; Landau zener mechnism; Quantum spin systems; Quntum dynamics; Quntum master equation; Quqntum computing

Indexed keywords

DZYALOSHINSKY-MORIYA INTERACTION; ESR; FLOQUET THEOREM; JAYENS-CUMMINGS MODEL; LANDAU-ZENER MECHNISM; QUANTUM SPIN SYSTEMS; QUNTUM DYNAMICS; QUNTUM MASTER EQUATION; QUQNTUM COMPUTING;

DYNAMICS; ELECTRON SPIN RESONANCE SPECTROSCOPY; LASER COOLING; QUANTUM ELECTRONICS; QUANTUM OPTICS; SPIN DYNAMICS; THEOREM PROVING;

REAL TIME SYSTEMS;

EID: 79955456959     PISSN: 15461955     EISSN: None     Source Type: Journal    
DOI: 10.1166/jctn.2011.1771     Document Type: Article

References (160)

1. M. Born and V. Fock, Z. Phys. 51, 165 (1928);
2. T. Kato, J. Phys. Soc. Jpn. 5, 435 (1950).
3. D. Gatteschi, R. Sessoli, and J. Villain, Molecular Nanomagnets, Oxford University Press (2006).
4. L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, and B. Barbara, Nature 383, 145 (1996);
5. J. R. Friedman, M. P. Sarachik, J. Tejada, and R. Ziolo, Phys. Rev. Lett. 76, 3830 (1996);
6. J.A.A. J. Perenboom, J. S. Brooks, S. Hill, T. Hathaway, and N. S. Dalai, Phys. Rev. B 58, 330 (1998);
7. T. Kubo, T. Goto, T. Koshiba, K. Takeda, and K. Awaga, Phys. Rev. B 65, 224425 (2002).
8. C. Sangregorio, T. Ohm, C. Paulsen, R. Sessoli, and D. Gatteschi, Phys. Rev. Lett. 78, 4645 (1997).
9. M. Ueda, S. Maegawa, and S. Kitagawa, Phys. Rev. B 66, 073309 (2002).
10. W. Wernsdorfer and R. Sessoli, Science 284, 233 (1999).
11. I. Chiorescu, W. Wernsdorfer, A. Miiller, H. Bogge, and B. Barbara, Phys. Rev. Lett. 84, 3454 (2000).
12. Rousochatzakis, Y. Ajiro, H. Mitamura, P. Kogerler, and M. Luban, Phys. Rev. Lett. 94, 147204 (2005).
13. K.-Y. Choi, Y. H. Matsuda, and H. Nojiri, Phys. Rev. Lett. 96, 107202 (2006).
14. Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, Nature 398, 786 (1999).
15. S. Bertaina, S. Gambarelli, T. Mitra, B. Tsukerblat, A. Miiller, and B. Barbara, Nature 453, 203 (2008).
16. T. Oka and H. Aoki, Phys. Rev. Lett. 95, 137601 (2005).
17. I. L. Chuang, N. Gershenfeld, and M. Kubinec, Phys. Rev. Lett. 81, 3408 (1998);
18. I. L. Chuang, L. M. K. Vandersypen, X. Zhou, D. W. Leung, and S. Lloyd, Nature 393, 143 (1998).
19. M. A. Nielsen and I. L. Chung, Quantum Computation and Quantum Information, Cambridge University Press (2000).
20. H. De Raedt and K. Michielsen, Handbook of Theoretical and Computational Nanotechnology, edited by M. Rieth and W. Schommers, American Scientific Publishers, Los Angeles (2006), pp. 2-44;
21. V. V. Dobrovitski and H. De Raedt, Phys. Rev. E 67, 056702 (2003).
22. L. Guner and B. Barbara (eds.), Quantum Tunneling of Magnetism, Series E: Appied Science, Nato Advanced Study Institute, Kluwer, Dordrecht (1995), Vol. 301;
23. E. M. Chudnovsky and L. Gunter, Phys. Rev. Lett. 60, 661 (1988);
24. Phys. Rev. B 37, 9455 (1988);
25. A. J. Legget, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
26. D. D. Awschalom, J. F. Smyth, G. Grinstein, D. P. DiVincenzo, and D. Loss, Phys. Rev. Lett. 68, 3092 (1992), ibid;
27. Phys. Rev. Lett. 70, 2199 (1993);
28. Phys. Rev. Lett. 71, 4279 (1993).
29. B. Barbara, C. Paulsen, L. C. Sampaio, M. Uehara, F. Fruchard, J. L. Tholence, and A. Marchand, Magnetic Properties of Fine Particles, edited by J. L. Dormann and D. Fiorani, Elsevier Science, Amsterdam (1992), p. 235.
30. L. D. Landau, Phys. Z. Sowjetunion 2, 46 (1932);
31. C. Zener, Proc. R. Soc. London A 137, 696 (1932);
32. E. C. G. Stueckelberg, Helv. Phys. Acta. 5, 369 (1932);
33. E. Majorana, Nuovo Cimento 9, 43 (1932).
34. S. Miyashita, J. Phys. Soc. Jpn. 64, 3207 (1995), and ibid;
35. J. Phys. Soc. Jpn. 65, 2734 (1996).
36. H. De Raedt, S. Miyashita, K. Saito, D. García-Pablos, and N. García, Phys. Rev. B 56, 11761 (1997).
37. A. Garg, Europhys. Lett. 22, 205 (1993).
38. K. Hijii and S. Miyashita, Phys. Rev. B 78, 214434 (2008).
39. K. Saito, S. Miyashita, and H. de Raedt, Phys. Rev. B 60, 14553 (1999).
40. Y. Shapira, M. T. Liu, S. Foner, C. E. Dube, and P. J. Bonitatebus, Phys. Rev. B 59, 1046 (1999).
41. H. Nakano and S. Miyashita, J. Phys. Soc. Jpn. 70, 2151 (2001);
42. H. Nakano and S. Miyashita, J. Phys. Chem. Solid. 63, 1519 (2002).
43. K. Saito and S. Miyashita, J. Phys. Soc. Jpn. 70, 3385 (2001).
44. I. E. Dzyloshinskii, Zh. Eksp. Thor. Fiz. 32, 1547 (1957);
45. Sov. Phys. JETP 5, 1259 (1957);
46. T. Moriya, Phys. Rev. 120, 91 (1960);
47. T. A. Kaplan, Z. Phys. B: Condens Matter 49, 313 (1983);
48. L. Shekhman, O. Entin-Wohlman, and A. Aharony, Phys. Rev. Lett. 69, 836 (1992);
49. L. Shekhman, A. Aharony, and O. Entin-Wohlman, Phys. Rev. B 47, 174 (1993).
50. S. Miyashita and N. Nagaosa, Prog. Theor. Phys. 106, 533 (2001).
51. H. De Raedt, S. Miyashita, K. Michielsen, and M. Machida, Phys. Rev. B 70, 064401 (2004).
52. S. Miyashita, S. Tanaka, H. de Raedt, and B. Barbara, J. Phys. Conf. Ser. 143, 012005 (2009).
53. S. Miyashita, H. De Raedt, and K. Michielsen, Prog. Theor. Phys. 110, 889 (2003);
54. B. K. Chakrabati, A. Dutta, and P. Sen, Quantum Ising Phase and Transverse Ising Models, Springer, Heidelberg (1996).
55. T. W. B. Kibble, J. Phys. A 9, 1387 (1976);
56. Phys. Rep. 67, 183 (1980);
57. W. H. Zurek, Nature (London) 317, 505 (1985);
58. Phys. Rep. 276, 177 (1996).
59. J. Dziarmaga, Phys. Rev. Lett. 95, 245701 (2005).
60. S. Miyashita, H. De Raedt, and B. Barbara, Phys. Rev. B 79, 104422 (2009).
61. J. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
62. B. A. Berg and T. Neuhaus, Phys. Lett. B 267, 249, (1991);
63. B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).
64. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).
65. R. H. Swendsen and J. S. Wang, Phys. Rev. Lett. 58, 86 (1987);
66. U. Wolff, Phys. Rev. Lett. 62, 361 (1989).
67. S. Geman and D. Geman, IEEE Trans. Pallern Anal. Mach. Intell. 6, 721 (1984).
68. T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998);
69. A. Das and B. K. Chakrabarti, Quantum Annealing and Related Optimization Methods, Springer, New York (2005);
70. G. E. Santoro and E. Tosatti, J. Phys. A 39, R393 (2006);
71. A. Das and B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061 (2008).
72. S. Morita and H. Nishimori, J. Phys. A 39, 13903 (2006);
73. S. Morita and H. Nishimori, J. Phys. Soc. Jpn. 76, 064002 (2007).
74. S. Morita, J. Phys. Soc. Jpn. 76, 104401 (2007).
75. S. Tanaka and S. Miyashita, Phys. Rev. E 81, 051138 (2010).
76. J. H. Shirley, Phys. Rev. 138, 979 (1965).
77. M. Grifoni and P. Hänggi, Phys. Rep. 304, 229 (1998).
78. S. Kohler, J. Lehmann, and P. Hänggi, Phys. Rep. 406, 379 (2005).
79. I. I. Rabi, Phys. Rev. 51, 652 (1937).
80. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, Dover, New York (1987).
81. P. K. Aravind and J. O. Hirschfelder, J. Phys. Chem. 88, 4788 (1984).
82. C. E. Creffield, Phys. Rev. B 67, 165301 (2003).
83. K. Saito and Y. Kayanuma, Phys. Rev. B 70, 201304(R) (2004).
84. S. Ashhab, J. R. Johansson, A. M. Zagoskin, and F. Nori, Phys. Rev. A 75, 063414 (2007).
85. Y. B. Zeldovisch, Eksp. Teor. Fiz. 51, 1492 (1966);
86. Sov. Phys.-JETP 24, 1006 (1967).
87. V. I. Ritus, Zh. Eksp. Teor. Fiz. 51, 1544, (1966);
88. Sov. Phys.-JETP 24, 1041 (1967).
89. H. Sambe, Phys. Rev. A 7, 2203 (1973).
90. F. Grossmann, T. Dittrich, P. Jung, and P. Hänggi, Phys. Rev. Lett. 67, 516 (1991).
91. F. Grossmann, P. Jung, T. Dittrich, and P. Hänggi, Z. Phys. B -Cond. Matt. 84, 315 (1991).
92. Y. Kayanuma, Phys. Rev. A 50, 843 (1994).
93. D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
94. Y. Kayanuma and K. Saito, Phys. Rev. A 11, 010101(R) (2008).
95. A. Eckardt, C. Weiss, and M. Holthaus, Phys. Rev. Lett. 95, 260404 (2005).
96. M. Sillanpäa, T. Lehtinen, A. Paila, Y. Makhlin, and P. Hakonen, Phys. Rev. Lett. 96, 187002 (2006).
97. M. G. Floquet, Ann. Ec. Norm. Suppl. 12, 47 (1883).
98. Y. Aharonov and J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).
99. Y. Kayanuma, Phys. Rev. A 55, R2495 (1997).
100. S. Miyashita, K. Saito, and H. De Raedt, Phys. Rev. Lett. 80, 1525 (1998);
101. Y. Teranishi and H. Nakamura, Phys. Rev. Lett. 81, 2032 (1998).
102. G. Ramon and X. Hu, Phys. Rev. B 75, 161301(R) (2007).
103. K. Hijii and S. Miyashita, Phys. Rev. A 81, 013403 (2010).
104. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Pergamon, Oxford (1976).
105. K. Drese and M. Holthaus, Euro. Phys. J. D 5, 119 (1999).
106. S. Guerin and H. R. Jauslin, Adv. Chem. Phys. 125, 147 (2003).
107. Y. Kayanuma, Phys. Rev. B 47, 9940 (1998).
108. M. Nishino, H, Onishi, K. Yamaguchi, and S. Miyashita, Phys. Rev. B 62, 9463 (2000).
109. A. Hams, H. De Raedt, S. Miyashita, and K. Saito, Phys. Rev. B 62, 13880 (2000).
110. S. Miyashita and K. Saito, J. Phys. Soc. Jpn. 70, 3238 (2001).
111. J. Villain, J. Phys. C: Solid State Phys. 10, 1717 (1977).
112. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II, Springer-Verlag, New York (1085).
113. W. H. Louisell, Quantum Statistical Properties of Radiation, Wiley, New York (1973).
114. N. Hashitsume, F. Shibata, and M. Shingu, J. Stat. Phys. 17, 155 (1977);
115. F. Shibata, Y. Takahashi, and N. Hashitsume, J. Stat. Phys. 17, 171 (1977).
116. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957);
117. P. C. Martin and J. Schwinger, Phys. Rev. 115, 115 (1959).
118. A. O. Caldeira and A. J. Leggett, Ann. Phys. (NY) 149, 374 (1983).
119. H. Grabert, P. Schramn, and G. Ingold, Phys. Rep. 3, 115 (1988).
120. D. P. Visco, Jr. and S. Sen, Phys. Rev. E 57, 224 (1998).
121. K. Saito, S. Takesue, and S. Miyashita, Phys. Rev. E 61, 2397 (2000).
122. J. H. Van Vleck, Phys. Rev. 74, 1168 (1948).
123. R. Kubo and K. Tomita, J. Phys. Soc. Jpn. 9, 888 (1954).
124. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
125. M. Suzuki and R. Kubo, J. Phys. Soc. Jpn. 24, 51 (1968).
126. A. Abragam, Principles of Nuclear Magnetism, Oxford Press, London (1961), and cited therin.
127. S. Miyashita, T. Yoshino, and A. Ogasahara, J. Phys. Soc. Jpn. 68, 655 (1999).
128. A. Ogasahara and S. Miyshita, J. Phys. Soc. Jpn. 69, 4043 (2000).
129. S. Miyashita and A. Ogasahara, J. Phys. Soc. Jpn. 72, 2350 (2003).
130. A. Ogasahara and S. Miyashita, J. Phys. Soc. Jpn. Suppl. B 72, 44 (2003).
131. I. Affleck and M. Oshikawa, Phys. Rev. B 60, 1038 (1999).
132. M. Oshikawa and I. Affleck, Phys. Rev. Lett. 82, 5136 (1999).
133. K. Nagata and Y. Tazuke, J. Phys. Soc. Jpn. 32, 337 (1972).
134. E. C. G. Sudarshan, P. M. Mathews, and J. Rau, Phys. Rev. 121, 920 (1961);
135. A. Kossakowski, Rep. Math. Phys. 3, 247 (1972);
136. A. Kossakowski, Bull. Acad. Pol. Sci. Ser. Math. Astr. Phys. 20, 1021 (1972);
137. A. Kossakowski, Bull. Acad. Pol. Sci. Ser. Math. Astr. Phys. 21, 649 (1973);
138. G. Lindblad, Commun. Math. Phys. 48, 119 (1976);
139. V. Gorrini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976);
140. V. Gorrini, A. Frigerio, M. Verri, A. Kossakowski, and E. C. G. Sudarshan, Rep. Math. Phys. 13, 149 (1978).
141. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994).
142. A. Suarez, R. Silbey, and I. Oppenheim, J. Chem. Phys. 97, 5101 (1992).
143. P. Gaspard and M. Nagaoka, J. Chem. Phys. Ill, 5668 (1999).
144. C. Uchiyama, M. Aihara, M. Saeki, and S. Miyashita, Phys. Rev. E 80, 021128 (2009).
145. Y. Kaluzny, P. G. M. Gross, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 51, 1175 (1983).
146. G. S. Agarwal, Phys. Rev. Lett. 53, 1732 (1984).
147. S. Miyashita, H. Ezaki, and E. Hanamura, Phys. Rev. A 57, 2046 (1998).
148. S. Fujisawa, Master Thesis, The University of Tokyo (2010).
149. Y. Nagaoka, Phys. Rev. 147, 392 (1966).
150. S. Miyashita, Prog. Thoer. Phys. 120, 785 (2008).
151. R. H. Dicke, Phys. Rev. 93, 99 (1954).
152. S. Miyashita, J. Phys. Soc. Jpn. 76, 104003 (2007).
153. C. F. Bharucha, K. W. Madison, P. R. Morrow, S. R. Wilkinson, Bala Sundaram, and M. G. Raizen, Phys. Rev. A 55, R857 (1997).
154. N. Hatano, K. Sasada, H. Nakamura, and T. Petrosky, Prog. Theor. Phys. 119, 187 (2008).
155. Y. Teranishi, N. Hatano, and Miyashita, unpublished.
156. S. Yuan, H. De Raedt, and S. Miyashita J. Phys. Soc. Jpn. 75, 084703 (2006);
157. S. Yuan, H. De Raedt, and S. Miyashita Phys. Rev. B 75, 184305 (2007).
158. N. V. Vitanov, Phys. Rev. A 59, 988 (1999);
159. K. Saito and Y. Kayanuma, Phys. Rev. A 65, 033407 (2002).
160. H. De Raedt, K. Michielsen, A. Hams, S. Miyashita, and K. Saito, Eur. Phys. J. B 27, 15 (2002).