Abstract
A new mechanism is described for producing slow decays in the velocity correlation function of diffusive systems with directed trapping. If the directions for entering and leaving a trap are correlated and if the distribution of trapping times has a long tail then the velocity correlation function will have a corresponding long time tail. This new long time tail decays liket −(2 +α), whereα is an exponent characterizing the tail of the distribution of trapping times. A simple random walk model which illustrates this mechanism is analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. H. Ernst, J. Machta, J. R. Dorfman and H. van Beijeren,J. Stat. Phys. 34:477 (1984).
J. Machta, M. H. Ernst, H. van Beijeren, and J. R. Dorfman,J. Stat. Phys. 35:413 (1984).
P. B. Visscher,Phys. Rev. B 29:5462 (1984);Phys. Rev. B 29:5472 (1984).
A. K. Harrison and R. Zwanzig,J. Stat. Phys. 42:935 (1986).
E. H. Hauge,Lecture Notes in Physics, No. 31, G. Kirczenow and J. Marro, eds. (Springer-Verlag, Berlin, 1974).
M. H. Ernst and A. Weijland,Phys. Lett. 34A:39 (1971).
C. Bruin,Physica 72:261 (1974).
B. J. Alder and W. E. Alley,Physica 121A:523 (1983).
T. R. Kirkpatrick and J. R. Dorfman,Phys. Rev. A 28:1022 (1983); W. Hoogeveen and J. A. Tjon,Physica 125A:163 (1984).
S. Alexander, J. Bernasconi, W. R. Schneider, and R. Orbach,Rev. Mod. Phys. 53:175 (1981); J. Machta,Phys. Rev. B 24:5260 (1981); R. Zwanzig,J. Stat. Phys. 28:127 (1982); H. van Beijeren,Rev. Mod. Phys. 54:195 (1982); J. W. Haus, K. W. Kehr, and K. Kitahara,Phys. Rev. B 25:4918 (1982); Th. M. Nieuwenhuizen and M. H. Ernst,Phys. Rev. B 31:3518 (1985).
J. W. Haus, K. W. Kehr, and J. W. Lyklema,Phys. Rev. B 25:2905 (1982).
J. Machta,J. Stat. Phys. 30:305 (1983).
P. J. H. Denteneer and M. H. Ernst,J. Phys. C 16:L961 (1983);Phys. Rev. B 29:1755 (1984).
J. Machta, M. Nelkin, Th. M. Nieuwenhuizen, and M. H. Ernst,Phys. Rev. B 31:7636 (1985).
G. H. Weiss,Separation Science and Technology 17:1609 (1983).
J. Machta and S. M. Moore, Diffusion and long time tails in the overlapping Lorentz gas,Phys. Rev. A 32:3164 (1985).
B. I. Halperin, S. Feng, and P. N. Sen,Phys. Rev. Lett. 54:2391 (1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Machta, J. Anomalous long time tails due to trapping. J Stat Phys 42, 941–948 (1986). https://doi.org/10.1007/BF01010455
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01010455