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APS » Journals » Phys. Rev. A » Volume 40 » Issue 11
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Phys. Rev. A 40, 6755–6758 (1989)

Diffusion in the presence of quenched random bias fields: A two-dimensional generalization of the Sinai model

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Robin L. Blumberg Selinger
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215

Shlomo Havlin
Division of Computers Research and Development, National Institutes of Health, Bethesda, Maryland 20892

François Leyvraz
Instituto de Fisica, Universidad Nacional Autónoma de México, Laboratorio de Cuernavaca, Apartado Postal 20-364, 01000 Mexico Distrito Federal, Mexico

Moshe Schwartz
Physics Department, Bar-Ilan University, 52 100 Ramat-Gan, Israel
School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69 978 Tel-Aviv, Israel

H. Eugene Stanley
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215

Received 21 August 1989; published in the issue dated December 1989

We report a theoretical and numerical study of diffusion in two dimensions in the presence of quenched random bias fields. The local bias field is taken to be the gradient of a random scalar potential V(i,j). We consider the special case V(i,j)=V1(i)+V2(j), where the gradients of V1 and V2 are chosen to be randomly ±ε0 with 0<ε0≤1. We find that asymptotically (t→∞) the mean square displacement grows with the time t as (lnt)4, just as in the one-dimensional Sinai model.

© 1989 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.40.6755
DOI:
10.1103/PhysRevA.40.6755
PACS:
05.30.-d
 
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