Weak subordination breaking for the quenched trap model

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.