Abstract
Recently non-Markoffian properties have been studied in various linear dissipative phenomena. Markoffian theories assume that the time scale of the process of our interest is distinctly larger than the time scales involved in underlying processes [1]. If the process is not Markoffian, then we usually try to find Markoffian equations by choosing a new set of variables. Very often we can succeed in doing this just by adding new variables. Thus Markoffian equations have been constructed and used successfully in many problems. Recently, however, there begins to appear interesting phenomena which cannot be described by linear Markoffian equations. For example, we now have interesting high-frequency phenomena with short wavelengths where no simple hydrodynamic description holds. Another example is provided by anomalous transport phenomena near critical points where a nonlinear coupling among macroscopic modes seems to play a crucial role.
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References
Chandrasekhar, S.: Rev. Mod. Phys.15, 1 (1943).
Wang, M. C. and Uhlenbeck, G. E.: Rev. Mod. Phys.17, 323 (1945).
Dorfman, J. R. and Cohen, E. G. D.: Phys. Rev. Letters25, 1257 (1970).
Ernst, M. H., Hauge, E. H., and van Leeuwen, J. M. J.: Phys. Rev. Letters25, 1254 (1970).
Pomeau, Y.: Phys. Rev.A3, 1174 (1971).
van Hove, L.: Phys. Rev.95, 1374 (1954).
Kubo, R. and Tomita, K.: J. Phys. Soc. Japan9, 888 (1954).
Kubo, R.: J. Phys. Soc. Japan12, 570 (1957).
Kadanoff, L. P. and Martin, P. C.: Ann. Phys.24, 419 (1963).
Mori, H.: Prog. Theor. Phys.33, 423 (1965).
Kawasaki, K.: Ann. Phys.61, 1 (1970).
Kawasaki, K.: paper presented at the International Conference on Statistical Mechanics, Univ. of Chicago, Chicago, 1971, and the references cited therein.
Zwanzig, R.: paper presented at the International Conference on Statistical Mechanics, Univ. of Chicago, 1971.
Heitler, W.: Quantum Theory of radiation. Oxford 1954.
Kohn, W. and Luttinger, J. M.: Phys. Rev.108, 590 (1957).
Zwanzig, R.: J. Chem. Phys.33, 1338 (1960).
In Ref. [5]the inner preduct is denoted by (F, G*).
Mori, H. and Okamoto, H.: Prog. Theor. Phys.40, 1287 (1968).
Zwanzig, R.: Phys. Rev.124, 983 (1961).
Dorfman, J. R. and Cohen, E. G. D.: Phys. Rev. Letters25, 1257 (1970).
Ernst, M. H., Hauge, E. H., and van Leeuwen, J. M. J.: Phys. Rev. Letters25, 1254 (1970).
Pomeau, Y.: Phys. Rev.A3, 1174 (1971).
Kawasaki, K.: Phys. Letters 32A, 379 (1970)
Kawasaki, K.: Phys. Letters 34A, 12 (1971).
Kawasaki, K.: J. Phys. Chem. Solids, 281277 (1967).
Résibois, P. and DeLeener, M.: Phys. Rev.152, 305 (1968)
Résibois, P. and DeLeener, M.: Phys. Rev.152, 318 (1968).
Wegner, F.: Z. Physik216, 433 (1968).
Blume, M. and Hubbard, J.: Phys. Rev.B1, 3815 (1970).
Hubbard, J.: J. App. Phys.42, 1390 (1971).
Mori, H.: Prog. Theor. Phys.34, 399 (1965).
Dupuis, M.: Prog. Theor. Phys.37, 502 (1967).
Sears, V. F.: Can. J. Phys.47, 199 (1969)
Sears, V. F.: Can. J. Phys.48, 616 (1970).
Lovesey, S. W.: J. Phys. (C)4, 3057 (1971).Lovesey, S. W. and Meserve, R. A.: a preprint. Tomita, H. and Mashiyama, H.: a preprint.
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Mori, H. (1973). Theory of Linear Non-Markoffian Processes. In: Haken, H. (eds) Synergetics. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-01511-6_5
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DOI: https://doi.org/10.1007/978-3-663-01511-6_5
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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