Asymptotically exact probability distribution for the Sinai model with finite drift

Woods, Gareth, Yurkevich, Igor, Lerner, Igor V. and Kovtun, H.A. (2010). Asymptotically exact probability distribution for the Sinai model with finite drift. Physical Review E, 82 (3),

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)
Published Date: 2010-09-17
Authors: Woods, Gareth
Yurkevich, Igor ( 0000-0003-1447-8913)
Lerner, Igor V.
Kovtun, H.A.

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Version: Accepted Version


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