Title: 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.