From Quenched Disorder to Continuous Time Random Walk

Stanislav Burov

Published 2017-07-17Version 1

This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to t/\Lambda^\alpha$ for transient process on translationally invariant lattice, in the sub-diffusive regime, is sufficient for asymptotic mapping. Exact form of the constant $\Lambda^\alpha$ is established. Disorder averaged position probability density function for quenched trap model is obtained and analytic expressions for the diffusion coefficient and drift are provided.