Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift

Details Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift

2002-09-04

arxiv.org/abs/cond-mat/0209078v1

Phys. Rev. E 66, 061105 (2002)

Physics

Condensed Matter

Statistical Mechanics

17 pages, two eps figures (included)

Scientific paper

10.1103/PhysRevE.66.061105

We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the energy spectrum of a single particle quantum Hamiltonian, which can be subsequently found. Our method allows us analytical access to arbitrary values of the drift (bias), thus going beyond the previous methods which provide results only in the limit of vanishing drift. We show that on varying the drift, the persistence displays a variety of rich asymptotic behaviors including, in particular, interesting qualitative changes at some special values of the drift.

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