Unified projection operator formalism in nonequilibrium statistical mechanics

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 3, 1999, Pages 2636-2650

  Uchiyama, Chikako ^a,b   Shibata, Fumiaki ^a,b  

^a UNIVERSITY OF YAMANASHI   (Japan)

^b OCHANOMIZU UNIVERSITY   (Japan)

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ARTICLE;

EID: 4244001475     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.2636     Document Type: Article

References (49)

1. J. M. Millar, A. M. Thayer, A. Bielecki, D. B. Zax, and A. Pines, J. Chem. Phys. 83, 934 (1985).
2. A. Bielecki, D. B. Zax, A. M. Thayer, J. M. Millar, and A. Pines, Z. Naturforsch. Teil A 41A, 440 (1986).
3. A. M. Thayer and A. Pines, J. Magn. Reson. 70, 518 (1986).
4. T. P. Jarvie, K. Takegoshi, D. Suter, and A. Pines, Chem. Phys. Lett. 158, 325 (1989).
5. E. Tönsing, H. Jung, C. Tempelmann, and H. Brömer, J. Magn. Magn. Mater. 97, 316 (1991).
6. V. A. Tulin, A. H. Vuorimäki, and E. E. Ylinen, J. Magn. Magn. Mater. 174, 137 (1997).
7. R. S. Hayano, Y. J. Uemura, J. Imazato, N. Nishida, T. Yamazaki, and R. Kubo, Phys. Rev. B 20, 850 (1979).
8. Y. Todate, N. Ohnishi, M. Tanaka, K. Nishiyama, and K. Nagamine, Hyperfine Interact. 104, 375 (1997).
9. T. Yamazaki, Hyperfine Interact. 104, 3 (1997).
10. R. I. Bewley and R. Cywinski, Phys. Rev. B 58, 11 544 (1998).
11. W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Clarendon Press, Oxford, 1954).
12. S. Nakajima, Prog. Theor. Phys. 20, 948 (1958).
13. R. Zwanzig, J. Chem. Phys. 33, 1338 (1960).
14. F. Haake, in Quantum Statistics in Optics and Solid-State Physics, edited by G. Höhler, Springer Tracts in Modern Physics Vol. 66 (Springer, Berlin, 1973), p. 98, and references cited therein.
15. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer-Verlag, Berlin, 1978).
16. F. Shibata, Y. Takahashi, and N. Hashitsume, J. Stat. Phys. 17, 171 (1977).
17. N. Hashitsume, F. Shibata, and M. Shingu, J. Stat. Phys. 17, 155 (1977).
18. T. Shimizu, J. Phys. Soc. Jpn. 28, 1088 (1970).
19. A. R. Altenberger and J. Stecki, J. Stat. Phys. 5, 83 (1972).
20. V. P. Vstovsky, J. Stat. Phys. 15, 105 (1976).
21. P. Mazur and I. Oppenheim, Physica (Amsterdam) 50, 241 (1970).
22. R. F. Fox, Phys. Rep. 48, 179 (1978).
23. S. Chaturvedi and F. Shibata, Z. Phys. B 35, 297 (1979).
24. F. Shibata and T. Arimitsu, J. Phys. Soc. Jpn. 49, 891 (1980).
25. See, for instance, H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer-Verlag, Berlin, 1989).
26. F. Shibata and I. Sato, Physica A 143, 468 (1987).
27. H. Mori, Prog. Theor. Phys. 33, 423 (1965).
28. M. Tokuyama and H. Mori, Prog. Theor. Phys. 55, 411 (1976).
29. S. A. Adelman, Adv. Chem. Phys. 48, 61 (1983).
30. J. Peřina, Jr., Physica A 214, 309 (1995).
31. K. Kawasaki, J. Phys. A 6, 1289 (1973).
32. K. Nemoto and F. Shibata, J. Phys. Soc. Jpn. 66, 3492 (1996).
33. C. Uchiyama and F. Shibata, J. Phys. Soc. Jpn. 65, 887 (1996).
34. P. W. Anderson, J. Phys. Soc. Jpn. 9, 316 (1954).
35. R. Kubo, J. Phys. Soc. Jpn. 9, 935 (1954).
36. R. Kubo, in Fluctuation, Relaxation, and Resonance in Magnetic Systems, edited by D. ter Haar (Oliver and Boyd, Edinburgh, 1962), p. 23.
37. R. Kubo, in Stochastic Process in Chemical Physics, edited by K. Shuler (John Wiley & Sons, New York 1969), p. 101.
38. E. Fick and G. Sauermann, The Quantum Statistics of Dynamical Processes (Springer, Berlin, 1990), p. 310.
39. A. Fuliński and W. J. Kramarczeyk, Physica (Amsterdam) 39, 575 (1968).
40. H. Gzyl, J. Stat. Phys. 26, 803 (1981).
41. N. Hashitsume, in Proceedings of the International Conference on Theoretical Physics, Kyoto and Tokyo, Sept. 1953, edited by I. Imai, Science Council of Japan, Tokyo, 1954), p. 495.
42. N. Hashitsume, Prog. Theor. Phys. 15, 369 (1956).
43. K. Someda and R. D. Levine, Chem. Phys. 184, 187 (1994).
44. R. Kubo, J. Math. Phys. 4, 174 (1963).
45. N. G. van Kampen, Physica (Amsterdam) 74, 215 (1974).
46. N. G. van Kampen, Physica (Amsterdam) 74, 239 (1974).
47. S. Chaturvedi, Phys. Lett. 66A, 443 (1978).
48. A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983).
49. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, Anupam Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).