J. Phys. Soc. Jpn. 64 (1995) pp. 93-98 |Next Article| |Table of Contents|
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Analysis on Hierarchical Equations of Mori and Tri-Diagonal Recurrence Relations
Fumiaki Shibata,
Mari Yasufuku and
Chikako Uchiyama 1,2
Department of Physics, Faculty of Science,
Ochanomizu University, Bunkyo-ku, Tokyo 112
1Department of Electrical Engineering and Computer Science,
Faculty of Engineering, Yamanashi University,
Kofu 400
2The Institute of Physical and Chemical Research (RIKEN),
Wako 350-01
(Received July 25, 1994)
A mathematical correspondence is established between a set
of equations due to Mori formalism and those of generalized
tri-diagonal recurrence relations.
Thus, once a set of coupled equations describing physical phenomena are
given, the corresponding Langevin equations can be obtained directly.
This enables us to construct a hierarchical structure of physical variables
and time scales
©1995 The Physical Society of Japan
KEYWORDS:
Mori formalism, tri-diagonal relation, memory effect,
separation of time-scale
URL:
http://jpsj.ipap.jp/link?JPSJ/64/93/
DOI: 10.1143/JPSJ.64.93
- H. Mori: Prog. Theor. Phys. 33 (1965) 423[IPAP].
- H. Mori: Prog. Theor. Phys. 34 (1965) 399[IPAP].
- F. Lado, J. D. Memory and G. W. Parker:
Phys. Rev, B4 (1971) 1406[APS].
- M. Howard Lee:
Phys. Rev. B26 (1982) 2547[APS].
- M. Ferrario and P. Grigolini:
J. Math. Phys. 20 (1979) 2567[AIP Scitation].
- See for instance, H. Risken: The Fokker-Planck Equation (Springer-Verlag, Berlin, Heidelberg, New York, 1989) 2nd ed.
