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-alpha = Sigma(infinity)(x--infinity)(n(x))(alpha), with n(x) being the number of visits to site x. Here 0 < alpha = 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-alpha is changed to laboratory time t with a Levy time transformation. Investigation of Brownian motion stopped at time S-alpha yields the diffusion front of the quenched trap model, which is favorably compared with numerical simulations. In the zero-temperature limit of alpha -> 0 we recover the renormalization group solution obtained by Monthus [Phys. Rev. E 68, 036114 (2003)]. Our theory surmounts the critical slowing down that is found when alpha -> 1. Above the critical dimension 2, mapping the problem to a continuous time random walk becomes feasible, though still not trivial.