Abstract
We study classical diffusion of particles in random media. Although many of our results are general, we focus on the case of an ion in a three-dimensional medium with random, quenched charge centers obeying bulk charge neutrality. Within a functional-integral framework, we calculate the effective diffusion coefficients by first-order and second-order self-consistent perturbation theory (with a Gaussian reference in both cases). We also carry out a one-loop order momentum space renormalization group calculation. The self-consistent methods are complicated numerically and fail beyond intermediate disorder strengths. In contrast, the renormalization group calculation gives an analytical result that appears valid even to high disorder strengths. The methodology, generally applicable to a quantitative calculation of effective diffusion coefficients in disordered media, resolves deficiencies in self-consistent perturbation theory approaches to this class of problems.
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References
P. C. Martin, E. D. Siggia, and H. A. Rose,Phys. Rev. A 8:423 (1973).
C. De Dominicis and L. Peliti,Phys. Rev. B 18:353 (1978); C. De Dominicis,Phys. Rev. B 18:4913 (1978).
J.-P. Bouchaud and A. Georges,Phys. Rep. C 195:127 (1990).
A. K. Chakraborty, D. Bratko, and D. Chandler,J. Chem. Phys. 100:1528 (1994).
R. P. Feynman,Statistical Mechanics: A Set of Lectures (Addison-Wesley, New York, 1972), Sections 2.11 and 3.4.
J.-P. Bouchaud and M. E. Cates,Phys. Rev. E 47:1455 (1993).
J. des Cloizeaux and G. Jannink,Polymers in Solution: Their Modeling and Structure (Oxford University Press, New York, 1990), Section 8.1.4.2.
R. J. Creswick, H. A. Farach, and C. P. Poole, Jr.:Introduction to Renormalization Group Methods in Physics (Wiley, New York, 1992), especially Section 9.8.
A. de Masi, P. A. Ferrari, S. Goldstein, and W. D. Wick,J. Stat. Phys. 55: 787 (1989), Eq. (6.39).
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling,Numerical Recipes in Fortran 2nd ed. (Cambridge University Press, New York, 1992), Section 4.5.
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Deem, M.W., Chandler, D. Classical diffusion in strong random media. J Stat Phys 76, 911–927 (1994). https://doi.org/10.1007/BF02188692
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DOI: https://doi.org/10.1007/BF02188692