From Quenched Disorder to Continuous Time Random Walk

Abstract: 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: $t\to t/\Lambda^{1/\alpha}$ for transient process on translationally invariant lattice, in the sub-diffusive regime, is sufficient for asymptotic mapping. Exact form of the constant $\Lambda^{1/\alpha}$ 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.