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In this work the diffusion in the quenched trap model with diverging meanwaiting times is examined. The approach of randomly stopped time is extensivelyapplied in order to obtain asymptotically exact representation of the disorderaveraged positional probability density function. We establish that thedimensionality and the geometric properties of the lattice, on top of which thedisorder is imposed, dictate the plausibility of a mean-filed approximationthat will only include annealed disorder. Specifically, for any case when theprobability to return to the origin ($Q_0$) is less than $1$, i.e. thetransient case, the quenched trap model can be mapped on to the continuous timerandom walk. The explicit form of the mapping is provided. In the case when anexternal force is applied on a tracer particle in a media described by thequenched trap model, the response to such force is calculated and a non-linearresponse for sufficiently low dimensionality is observed.

The Transient Case of The Quenched Trap Model