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Woods, Gareth; Yurkevich, Igor; Lerner, Igor V.; Kovtun, H.A. (2010)
Languages: English
Types: Article
Subjects: Condensed Matter - Statistical Mechanics
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, 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.
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