## 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.

Original language | English |
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Article number | 30103 |

Number of pages | 4 |

Journal | Physical Review E |

Volume | 82 |

Issue number | 3 |

DOIs | |

Publication status | Published - 17 Sept 2010 |