Derivation of Langevin equation from microscopic theory

Physica A: Statistical Mechanics and its Applications

Volumn 276, Issue 1, 2000, Pages 164-187

  Wakou, J ^a   Koide, J ^a   Fukuda, R ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS;

CLOSED TIME PATH FORMALISM; FIELD THEORY; LANGEVIN EQUATION; MICROSCOPIC HAMILTONIAN;

STATISTICAL MECHANICS;

EID: 0033894505     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(99)00363-5     Document Type: Article

References (48)

1. See e.g., N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981.
2. C.W. Gardiner, Handbook of Stochastic Methods, Springer, Berlin, 1983.
3. R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II, Springer, Berlin, 1985.
4. U. Weiss, Quantum Dissipative Systems, World Scientific, Singapore, 1993.
5. V.B. Magalinskii, Zh. Eksp. Teor. Fiz. 36 (1959) 1942 [Sov. Phys. JETP 9 (1959) 1381].
6. V.B. Magalinskii, Zh. Eksp. Teor. Fiz. 36 (1959) 1942 [Sov. Phys. JETP 9 (1959) 1381].
7. Ullersma P. Physica. 32:1966;27.
8. Ullersma P. Physica. 32:1966;56.
9. Ullersma P. Physica. 32:1966;74.
10. Mori H. Prog. Theor. Phys. 33:1965;423.
11. Mori H. Prog. Theor. Phys. 34:1965;399.
12. H. Grabert, Projection Operator Techniques in Non-equilibrium Statistical Mechanics, Springer, Berlin, 1982.
13. Wells W.H. Ann. Phys. (USA). 12:1961;1.
14. Schmid A. J. Low Temp. Phys. 49:1982;609.
15. Hashitsume N., Mori M., Takahashi T. J. Phys. Soc. Jpn. 55:1986;1887.
16. Senitzky I.R. Phys. Rev. 119:1960;670.
17. Ford G.W., Kac M., Mazur P. J. Math. Phys. 6:1965;504.
18. Benguria R., Kac M. Phys. Rev. Lett. 46:1981;1.
19. Ford G.W., Kac M. J. Stat. Phys. 46:1987;803.
20. Gardiner C.W. IBM J. Res. Dev. 32:1988;127.
21. Zhou G.-Z., Su Z.-B., Hao B.-L., Yu L. Acta Phys. Sinica. 29:1980;961.
22. Zhou G.-Z., Hao B.-L., Yu L. Acta Phys. Sinica. 29:1980;969.
23. Zhou G.-Z., Su Z.-B., Hao B.-L., Yu L. Phys. Rev. B. 22:1980;3385.
24. M. Sumino, R. Fukuda, H. Higurashi, Prog. Theor. Phys. 86 (1991) 617, see also [32].
25. N.G. van Kampen, Can. J. Phys. 39 (1961) 551, see also Ref. [1].
26. R. Kubo, K. Matsuo, K. Kitahara, J. Stat. Phys. 9 (1973) 51.
27. Schwinger J. J. Math. Phys. 2:1961;407.
28. L.V. Keldysh, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018].
29. L.V. Keldysh, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018].
30. Niemi A.J., Semenoff G.W. Ann. Phys. 152:1984;105.
31. Rammer J., Smith H. Rev. Mod. Phys. 58:1986;323.
32. Landsman N.P., van Weert Ch.G. Phys. Rep. 145:1987;141.
33. Chou K.-C., Su Z.-B., Hao B.-L., Yu L. Phys. Rep. 118:1985;1.
34. Fukuda R., Komachiya M., Yokojima S., Suzuki Y., Okumura K., Inagaki T. Prog. Theor. Phys. Suppl. 121:1995;1.
35. M. Sumino, R. Fukuda, J. Phys. Soc. Jpn. 59 (1990) 3553, see also [32].
36. Green M.S. J. Chem. Phys. 20:1952;1281.
37. J.J. Binney, N.J. Dowrick, A.J. Fisher, M.E.J. Newman, The Theory of Critical Phenomena, Clarendon Press, Oxford, 1993.
38. Janssen H.K. Z. Phys. B. 23:1976;377.
39. C. De Dominicis, J. Phys. (Paris) Colloque. 37 (1976) 247.
40. R. Bausch, H.K. Janssen, H. Wagner, J. Phys. (Paris) Colloque. 24 (1976) 113.
41. De Dominicis C., Peliti L. Phys. Rev. B. 18:1978;353.
42. R. Fukuda, M. Sumino, Phys. Rev. A 44 (1991) 6252, see also [32].
43. R. Kubo, Rep. Progr. Phys. (London) 29 (1966) Part1 255.
44. R. Kubo (Ed.), Tokyo Summer Lectures in Theoretical Physics, 1965, Part1, Many-Body Theory, Shokabo, Tokyo, and Benjamin, New York, 1965, p. 1.
45. Callen H.B., Welton T.A. Phys. Rev. 83:1951;34.
46. Onsager L., Machlup S. Phys. Rev. 91:1953;1505.
47. Machlup S., Onsager L. Phys. Rev. 91:1953;1512.
48. J. Koide, to appear in Prog. Theor. Phys. 102 (1999).