Projects per year
Abstract
We obtain the exact asymptotic result for the disorderaveraged 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 imaginarytime 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 longtime asymptotic behavior.
Original language  English 

Pages (fromto)  030103 
Number of pages  1 
Journal  Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 
Volume  82 
Issue number  3 
DOIs  
Publication status  Published  1 Sept 2010 
Projects
 1 Finished

FieldTheoretical to Complex Networks
Engineering & Physical Science Research Council
1/02/08 → 31/07/11
Project: Research Councils