## 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 language | English |
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Article number | 041137 |

Pages (from-to) | 041137 |

Journal | Physical Review E |

Volume | 86 |

Issue number | 4 |

DOIs | |

State | Published - 19 Oct 2012 |