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.
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This work was supported by the Pazy Research Foundation. I thank E. Barkai for many discussions.
© 2017 American Physical Society.