Weak subordination breaking for the quenched trap model

S. Burov, E. Barkai

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Abstract

We map the problem of diffusion in the quenched trap model onto a different stochastic process: Brownian motion that is terminated at the coverage time S α=x=-( x )α, with n x being the number of visits to site x. Here 0<α=T/T g<1 is a measure of the disorder in the original model. This mapping allows us to treat the intricate correlations in the underlying random walk in the random environment. The operational time S α is changed to laboratory time t with a Lévy time transformation. Investigation of Brownian motion stopped at time S α yields the diffusion front of the quenched trap model, which is favorably compared with numerical simulations. In the zero-temperature limit of α→0 we recover the renormalization group solution obtained by Monthus. Our theory surmounts the critical slowing down that is found when α→1. Above the critical dimension 2, mapping the problem to a continuous time random walk becomes feasible, though still not trivial.

Original languageEnglish
Article number041137
JournalPhysical Review E
Volume86
Issue number4
DOIs
StatePublished - 19 Oct 2012

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