Long time tails in stationary random media II: Applications
Tóm tắt
In a previous paper we developed a mode-coupling theory to describe the long time properties of diffusion in stationary, statistically homogeneous, random media. Here the general theory is applied to deterministic and stochastic Lorentz models and several hopping models. The mode-coupling theory predicts that the amplitudes of the long time tails for these systems are determined by spatial fluctuations in a coarse-grained diffusion coefficient and a coarse-grained free volume. For one-dimensional models these amplitudes can be evaluated, and the mode-coupling theory is shown to agree with exact solutions obtained for these models. For higher-dimensional Lorentz models the formal theory yields expressions which are difficult to evaluate. For these models we develop an approximation scheme based upon projecting fluctuations in the diffusion coefficient and free volume onto fluctuations in the density of scatterers.
Tài liệu tham khảo
M. H. Ernst, J. Machta, J. R. Dorfman, and H. van Beijeren,J. Stat. Phys. (1984).
P. Grassberger,Physica 103A:558 (1980).
H. van Beijeren,Rev. Mod. Phys. 54:195 (1982).
H. Spohn and H. van Beijeren,J. Stat. Phys. 31:231 (1983).
M. H. Ernst and H. van Beijeren,J. Stat. Phys. 26:1 (1981).
P. M. Richards and R. L. Renken,Phys. Rev. B 21:3740 (1981).
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).
J. Machta,J. Stat. Phys. 30:305 (1983).
J. W. Haus, K. W. Kehr, and K. Kitahara,Phys. Rev. B 25:4918 (1982);Z. Phys. B50:161 (1983).
I. Webman and J. Klafter,Phys. Rev. B 26:5950 (1982).
M. J. Stephen and R. Kariotis,Phys. Rev. B 26:2917 (1982).
P. J. H. Denteneer and M. H. Ernst,J. Phys. C 16:L961 (1983).
J. W. Haus, K. W. Kehr, and J. Lyklema,Phys. Rev. B 25:2905 (1982).
V. Halpern,J. Phys. C 15:L827 (1982).
P. J. H. Denteneer and M. H. Ernst,Phys. Rev. B 29:1755 (1984).
E. H. Hauge,Lecture Notes in Physics, G. Kirczenow and J. Marro, eds. (Springer Verlag, Berlin, 1974), Vol. 31.
J. L. Lebowitz, J. K. Percus, and L. Verlet,Phys. Rev. 153:250 (1967); D. C. Wallace and G. K. Straub,Phys. Rev. A 27:2201 (1983).
J. Kertesz,J. Phys. (Paris) Lett. 42:L395 (1981).
S. W. Haan and R. Zwanzig,J. Phys. A. Math. Gen. 10:1547 (1977).
E. T. Gawlinski and H. E. Stanley,J. Phys. A. Math. Gen. 14:L291 (1981).
A. Masters and T. Keyes,Phys. Rev. A 25:1010 (1982); 26:2129 (1982); T. Keyes,Physica 118A:395 (1983).
M. H. Ernst and A. Weyland,Phys. Lett. 34A:39 (1971).
J. M. J. van Leeuwen and A. Weyland,Physica 36:457 (1967);38:35 (1968).
W. Götze, E. Leutheuser, and S. Yip,Phys. Rev. A 23:2634 (1981);24:100 (1981);25:533 (1982).
T. Keyes and J. Mercer,Physica 95A:473 (1979).
C. Bruin,Phys. Rev. Lett. 29:1670 (1972);Physica 72:261 (1974).
W. E. Alley, Ph.D. thesis, Univ. Calif. Davis (1979).
B. J. Alder and W. E. Alley,J. Stat. Phys. 19:341 (1978).
B. J. Alder inLecture Notes in Physics, Vol. 84, L. Carrido, P. Seglar, and P. J. Shepherd, eds. (Springer, Berlin, 1978).
B. J. Alder and W. E. Alley, preprint, November (1981).
B. J. Alder and W. E. Alley,Phys. Rev. Lett. 43:653 (1979).
J. C. Lewis and J. A. Tjon,Phys. Lett. 66A:349 (1978).
J. C. Lewis, private communication.
F. H. Ree and W. G. Hoover,J. Chem. Phys. 40:939 (1964).
P. Visscher, private communication andPhys. Rev. B, to appear.