From quenched disorder to continuous time random walk

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→t/Λ1/α, for a transient process in the subdiffusive regime is sufficient for asymptotic mapping. An exact form of the constant Λ1/α is established. A disorder averaged position probability density function for a quenched trap model is obtained, and analytic expressions for the diffusion coefficient and drift are provided.