Prog. Theor. Phys. Vol. 58 No. 4 (1977) pp. 1127-1141

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Langevin Type Equations in Nonequilibrium State

— Derivation and Applications to Linear Response Theory and Scattering Cross Section —

Hiroshi Furukawa

Institute of Physical Sciences, Faculty of Education, Yamaguchi University, Yamaguchi 753

(Received November 11, 1976)

Abstract:

The generalizations of the Langevin equation and the fluctuation-dissipation theorem are discussed in nonequilibrium states. The existence of the general form of the fluctuation-dissipation theorem associated with the Langevin type equation in nonequilibrium states is shown on the basis of a kinematical consideration. The equation of motion for the average fluctuations of dynamical variables in the presence of external fields is discussed within the linear response theory and is reduced to a more useful form by means of the Langevin type equation. The scattering cross section of particles from a system of interacting particles in a nonequilibrium state is also considered in connection with the Langevin type equation.

URL : http://ptp.ipap.jp/link?PTP/58/1127/
DOI : 10.1143/PTP.58.1127

References:

R. Kubo, J. Phys. Soc. Jpn. 12 (1957), 570[JPSJ].
H. Mori, Prog. Theor. Phys. 33 (1965), 423[PTP].
N. G. van Kampen, in Fluctuation Phenomena in Solids, edited by R. E. Burgess (Academic Press, New York-London).
R. Kubo, K. Matsuo and K. Kitahara, J. Stat. Phys. 9 (1973), 51[CrossRef].
M. Suzuki, Prog. Theor. Phys. 53 (1975), 1657[PTP]; J. Stat. Phys. 14 (1976), 129; Prog. Theor. Phys. 55 (1976), 383[PTP].
H. Furukawa, Prog. Theor. Phys. 54 (1975), 370[PTP].
H. Furukawa, Prog. Theor. Phys. 56 (1976), 464[PTP].
M. Tokuyama and H. Mori, Prog. Theor. Phys. 55 (1976), 411[PTP].
H. Furukawa, Prog. Theor. Phys. 57 (1977), 333[PTP].
R. Kubo, in Tokyo Summer Lectures in Theoretical Physics, 1965 Part I, Many-Body Theory, edited by R. Kubo (Shokabo, Tokyo) and (Benjamin, New York); Rep. Prog. Phys. 29 (1966), 255[CrossRef].
L. van Hove, Phys. Rev. 95 (1954), 249[APS].
J. W. Cahn, Trans. Metall. Soc. AIME 242 (1968), 166.
J. S. Langer, Ann. of Phys. 65 (1971), 53[CrossRef].
K. Tomita and H. Tomita, Prog. Theor. Phys. 51 (1974), 1731[PTP].
K. Tomita, T. Ohta and H. Tomita, Prog. Theor. Phys. 52 (1974), 1744[PTP].
H. Mashiyama, A. Ito and T. Ohta, Prog. Theor. Phys. 54 (1975), 1050[PTP].
H. Mori, Prog. Theor. Phys. 53 (1975), 1617[PTP].
Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 54 (1975), 60[PTP].
N. Ohta and M. Suzuki, J. Phys. Soc. Jpn. 39 (1975), 1175[JPSJ].
S. Kabashima, M. Itsumi, T. Kawakubo and T. Nagashima, J. Phys. Soc. Jpn. 39 (1975), 1183[JPSJ].
T. Takagahara, Prog. Theor. Phys. 55 (1976), 48[PTP].
H. Fujisaka and H. Mori, Prog. Theor. Phys. 56 (1976), 754[PTP].
F. Shibata, Private communication.
R. Zwanzig, J. Chem. Phys. 33 (1960), 1338[CrossRef].

Citing Article(s) :

Progress of Theoretical Physics Vol. 59 No. 4 (1978) pp. 1072-1084 :
Time Evolution of Quenched Binary Alloy at Low Temperatures

Hiroshi Furukawa
Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 70-90 :
Study of Langevin Type Equations by Means of a New Projection Operator Method in Nonequilibrium States

Hiroshi Furukawa