Asymptotically exact probability distribution for the Sinai model with finite drift

Abstract

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, <x(n)> similar to v(mu n), where mu <1 is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schrodinger equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasicontinuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior.

Publication DOI: https://doi.org/10.1103/PhysRevE.82.030103
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: © 2010 The American Physical Society
Full Text Link: http://link.aps ... sRevE.82.030103
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2010-09-17
Authors: Woods, Gareth
Yurkevich, Igor ( 0000-0003-1447-8913)
Lerner, Igor V.
Kovtun, H.A.

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