Abstract
We compare two simple “cartoons” of relaxation processes in dipolar materials: the “first passage” relaxation function introduced by K. Weron (1991) and the “average” relaxation function expressing the proportion of dipoles which did not change their imposed aligned orientation up to a certain time, the latter providing a description closer to what is experimentally measured. In some cases, the two relaxation functions are proved to coincide.
Similar content being viewed by others
References
H. Scher, M. F. Shlesinger, and J. T. Bendler,Phys. Today 44:26 (1991).
J. Klafter and M. F. Shlesinger,Proc. Natl. Acad. Sci. USA 83:848 (1986).
R. Rammal,J. Phys. (Paris)46:1857 (1985).
M. F. Shlesinger and E. W. Montroll,Proc. Natl. Acad. Sci. USA 81:1280 (1984).
K. Weron,J. Phys.: Condens. Matter 3:9151 (1991).
K. Weron,J. Phys.: Condens. Matter 4:10507 (1992).
K. Weron and A. Jurlewicz,J. Phys. A.: Math. Gen. 26:395 (1993).
A. Jurlewicz and K. Weron,J. Stat. Phys. 73:69 (1993).
R. Friedberg and J. M. Luttinger,Phys. Rev. B 12:4460 (1975).
P. Grassberger and I. Procaccia,J. Chem. Phys. 77:6281 (1982).
J. C. Rasaiah and Jianjun Zhu,J. Chem. Phys. 93:5768 (1990).
M. D. Donsker and S. R. S. Varadhan,Commun. Pure Appl. Math. 28:525 (1975);32:721 (1979).
L. A. Dissado and R. M. Hill,Proc. Roy. Soc. A. 390:131 (1983).
A. K. Jonscher,Dielectric Relaxation in Solids (Chelsea Dielectric Press, London, 1983).
C. J. Böttcher and P. Bordewijk,Theory of Electronic Polarisation, Vol. 2 (Elsevier, Amsterdam, 1978).
P. Debye,Z. Phys. 13:97 (1912).
R. G. Palmer, D. Stein, E. S. Abrahams, and P. W. Anderson,Phys. Rev. Lett. 53: 958 (1984).
L. A. Dissado and R. M. Hill,Chem. Phys. 111:193 (1987).
E. W. Montroll and J. T. Bendler,J. Stat. Phys. 34:639 (1984).
B. V. Gnedenko and A. N. Kolmogorov,Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Reading, Massachusetts, 1954).
A. Janicki and A. Weron,Simulation and Chaotic Behavior of α-Stable Stochastic Processes (Marcel Dekker, New York, 1994).
J. Galambos,The Asymptotic Theory of Extreme Order Statistics (Wiley, New York, 1978).
M. R. Leadbetter, G. Lindgren, and H. Rootzen,Extremes and Related Properties of Random Sequences and Processes (Springer-Verlag, New York, 1983).
R. V. Hogg and S. A. Klugman,Loss Distributions (Wiley, New York, 1984).
A. Plonka,Ann. Rep. Prog. Chem. 89:37 (1992).
A. Blumen,Nuovo Cimento B 63:50 (1981).
G. Zumofen, A. Blumen, and J. Klafter,J. Chem. Phys. 83:3298 (1995).
G. A. Niklasson,J. Appl. Phys. 62:R1 (1987).
G. A. Niklasson,J. Phys.: Condens. Matter 5:4233 (1983).
A. Jonscher, Private communication (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Weron, A., Weron, K. & Woyczynski, W.A. Relaxation functions in dipolar materials. J Stat Phys 78, 1027–1038 (1995). https://doi.org/10.1007/BF02183699
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02183699