Abstract
The previous chapter treated Brownian motion as the most typical stochastic process in physics. This chapter goes further to discuss the basic ideas of how statistical problems are treated as stochastic processes. In particular, the concept of Markovian processes plays a very important role in physics and so it is treated in detail, including the conditions for its validity. A fundamental problem is how a physical process is treated when it is no longer regarded as Markovian. It is not possible to discuss this thoroughly but we shall touch on it also.
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References
P. W. Anderson, P. R. Weiss: Rev. Mod. Phys. 25, 269 (1954)
P. W. Anderson: J. Phys. Soc. Jpn. 9, 316 (1954)
R. Kubo: J. Phys. Soc. Jpn. 9, 935 (1954)
R. Kubo: In Fluctuation, Relaxation and Resonance in Magnetic Systems, ed. by D. ter Haar (Oliver and Boyd, London 1982); R. Kubo: In Stochastic Processes in Chemical Physics, ed. by K. Shuler (Wiley, New York 1969)
N. Bloembergen, E. M. Purcell, R. V. Pound: Phys. Rev. 70, 679 (1948); J. H. Van Vleck: Phys. Rev. 72, 1168 (1948)
R. Kubo: J. Math. Phys. 4, 174 (1962)
H. Kramers: Physica 7, 284 (1940)
W. Feller: An Introduction to Probability Theory, Vol. 1 2nd ed. (Wiley, New York 1962); J. L. Doob: Stochastic Processes (Wiley, New York 1953)
R. Kubo: In Perspectives in Statistical Physics, ed. by J. Ravechè (North-Holland, Amsterdam 1981)
A. Fokker: Dissertation, Leiden University (1913); Ann. Physik 43, (4) 810 (1914) M. Planck: Berl. Ber. p. 324 (1917); See references in G. E. Uhlenbeck, L. S. Ornstein: Phys. Rev. 36, 823 (1930); H. Risken: The Fokker-Planck Equation, Springer Ser. Syn., Vol. 18, 2nd edn. (Springer, Berlin, Heidelberg 1989)
K. Ito: Proc. Imp. Acad. Tokyo 20, 519 (1944); K. Ito, H. McKean, Jr.: Diffusion Processes and their Sample Paths (Springer, Berlin, Heidelberg, New York 1965)
R. Stratonovich: J. SIAM Control 4, 362 (1966)
R. E Mortensen: J. Stat. Phys. 1, 271 (1969); M. Suzuki: Prog. Theor. Phys. Suppl. 69, 160 (1980)
J. L. Doob: Ann. Am. Stat. 15, 229 (1944); Ann. Math. 43, 351 (1942); M. C. Wang, G. E. Uhlenbeck: Rev. Mod. Phys. 17, 323 (1945)
S. Nakajima: Prog. Theor. Phys. 20, 948 (1958); R. Zwanzig: J. Chem. Phys. 33, 1338 (1960); H. Mori: Prog. Theor. Phys. 33, 424 (1965); The projection operator method is essentially the same as the damping theory used in quantum mechanics: see W. Heitier: The Quantum Theory of Radiation, 2nd ed. (Oxford Univ. Press, Oxford 1944), and A. Messiah: Mechanique Quantique (Dunod, Paris 1959), Quantum Mechanics (North-Holland, Amsterdam 1961)
W. Pauli: In Probleme der Modernen Physik, Festschrift zum 60. Geburtstag A. Sommerfelds, ed. by P. Debye (Hirzel, Leipzig 1928)
L. Van Hove: Physica 21, 517 (1955); 23, 441 (1957); R. Brout, I. Prigogine: Physica 22, 621 (1956)
F. Englert: J. Phys. Chem. Solids 11, 78 (1959). This is probably the first formulation of this problem in the form of (2.7.24). There have been a great number of papers which repeat essentially the same thing.
W. Weidlich, F. Haake: Physik 185, 30 (1965)
L. Boltzmann: Vorlesungen über Gastheorie, 2 Bde. (Barth, Leipzig 1912); Lectures on Gas Theory (transi, by G. Brush) (Univ. of California Press, Berkeley 1964)
N. Bogolyubov: In Studies in Statistical Mechanics, Vol. 1 ed. by G. E. Uhlenbeck, J. Boer (North-Holland, Amsterdam 1962)
J. R. Dorfman: In Perspectives in Statistical Physics, ed. by H. J. Raveché (North-Holland, Amsterdam 1981), This is a recent review of the problem
L. D. Landau: J. Exp. Theor. Phys. (USSR) 30, 1058 (1956); Sov. Phys. 3, 920 (1957); D. Pines, P. Nozieres: The Theory of Quantum Liquids, Vol. 1 (Benjamin, New York 1966)
R. Mori: Prog. Theor. Phys. 33, 424 (1965)
R. Kubo: Rep. Prog. Phys. 29, Part I, 255 (1966)
J. Kirkwood: J. Chem. Phys. 14, 180 (1946)
M Huberman, G. V. Chester Adv. Phys. 24, 489 (1975) See also R. Kubo: In Transport Phenomena, ed. by G. Kirczenow and J. Maro, Lecture Notes Phys., Vol. 31 (Springer, Berlin, Heidelberg 1974)
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Kubo, R., Toda, M., Hashitsume, N. (1991). Physical Processes as Stochastic Processes. In: Statistical Physics II. Springer Series in Solid-State Sciences, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58244-8_2
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DOI: https://doi.org/10.1007/978-3-642-58244-8_2
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