Abstract
We calculate a correlation function of a dipole which flips upon contact with one of the defects making generally non-Gaussian diffusions. Other than the memory effect in the fractal random walk model, the non-Gaussian property can be an origin of the stretched-exponential law of the correlation function.
Similar content being viewed by others
References
T. V. Ramakrishnan and M. Raj Lakshmi,Non-Debye Relaxation in Condensed Matter (World Scientific, Singapore, 1987).
K. Murayama, inFractal Sciences, H. Takayasu, ed. (Asakura, Tokyo, 1987) [in Japanese].
J. Klafter and M. F. Shlesinger,Proc. Natl. Acad. Sci. USA 83:848 (1986), and references cited therein.
S. H. Glarum,J. Chem. Phys. 33:1371 (1960).
P. Bordewijk,Chem. Phys. Lett. 32:592 (1975).
S. Redner and K. Kang,J. Phys. A 17:L451 (1984); J. Klafter and A. Blumen,Chem. Phys. Lett. 119:377 (1985); G. Zumofen, A. Blumen, and J. Klafter,J. Chem. Phys. 82:3198 (1985).
M. Bramson and J. L. Lebowitz,Phys. Rev. Lett. 61:2397 (1988), and references cited therein.
R. Czech,Z. Phys. B 75:513 (1989).
E. W. Montroll and G. H. Weiss,J. Math. Phys. 6:167 (1965).
E. W. Montroll and H. Scher,J. Stat. Phys. 9:101 (1973).
E. W. Montroll and M. F. Shlesinger,Studies in Statistical Mechanics, Vol. XI (North-Holland, 1984), p. 1.
M. F. Shlesinger and E. W. Montroll,Proc. Natl. Acad. Sci. USA 81:1280 (1984).
W. H. Hamill and K. Funabashi,Phys. Rev. B 16:5523 (1977).
M. Tachiya,Rad. Phys. Chem. 17:447 (1981).
J. T. Bendler and M. F. Shlesinger,J. Stat. Phys. 53:531 (1988).
Y. Pomeau and P. Résibois,Phys. Rep. 19C:63 (1975).
Y. Okabe,J. Stat. Phys. 45:953 (1986); inLecture Notes in Mathematics, No. 1299 (1988), p. 391.
A. Inoue,J. Math. Soc. Jpn., to appear.
R. Graham and A. Schenzel,Phys. Rev. A 25:1731 (1982); L. Brenig and N. Banai,Physica 5D:208 (1982); K. Ishii and K. Kitahara,Prog. Theor. Phys. 68:665 (1982); M. Suzuki, K. Kaneko, and S. Takesue,Prog. Theor. Phys. 67:1756 (1982); M. Suzuki, S. Takesue, and F. Sasagawa,Prog. Theor. Phys. 68:98 (1982); K. Kitahara and K. Ishii,Prog. Theor. Phys. 70:312 (1983); M. Suzuki, inProceedings Taniguchi Symposium on Stochastic Analysis, K. Itô (Kinokuniya, Tokyo, 1984), p. 423.
N. Minami, Y. Ogura, and M. Tomisaki,Ann. Prob. 13:698 (1985).
Y. Ogura and M. Tomisaki, inStochastic Processes and their Applications, S. Albeverio, ed. (Kluwer, 1990), p. 245.
M. Tomisaki,J. Math. Soc. Jpn. 40:561 (1988).
K. Kawamura,Z. Phys. B 29:101 (1978);30:1 (1978).
H. Araki, K. Kitahara, and K. Nakazato,Prog. Theor. Phys. 66:1895 (1981).
Y. Irie and K. Kawamura,Prog. Theor. Phys. 70:674 (1983).
H. M. Ito, S. Kotani, and T. Yokota,J. Stat. Phys. 51:569 (1987).
K. Itô,Stochastic Processes II(Yale University Press, New Haven, Connecticut, 1963), Chapter 5.
K. Itô and H. P. McKean, Jr.,Diffusion Processes and Their Sample Paths, 2nd ed. (Springer, Berlin, 1974).
R. E. Greene and H. Wu,Function Theory on Manifolds Which Possesses a Pole (Springer, Berlin, 1979).
Y. Ogura,Rep. Fac. Sci. Eng. Saga Univ. 7:13 (1979).
M. Tomisaki,Sugaku 41:49 (1989) in Japanese; English translation,Sugaku, to appear.
N. Ikeda and S. Watanabe,Stochastic Differential Equations and Diffusion Processes (North-Holland/Kodansha, 1981), Chapter 4, Sections.
M. F. Shlesinger, J. Klafter, and Y. M. Wong,J. Stat. Phys. 27:499 (1982).
Z. Schuss,Theory and Applications of Stochastic Differential Equations (Wiley, 1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ito, H.M., Ogura, Y. & Tomisaki, M. Stretched-exponential decay laws of general defect diffusion models. J Stat Phys 66, 563–582 (1992). https://doi.org/10.1007/BF01060081
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01060081