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arXiv · 1007.5287

Asymptotically exact probability distribution for the Sinai model with finite drift

Gareth Woods·Igor V. Yurkevich·Igor V. Lerner·H. A. Kovtun
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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, ~ t^{\mu n} where \mu 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 Schr\"{odinger} equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasi-continuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior.

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Gareth Woods, Igor V. Yurkevich, Igor V. Lerner, H. A. Kovtun. 2010-07-29. Asymptotically exact probability distribution for the Sinai model with finite drift. https://doi.org/10.1103/physreve.82.030103

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