Time transformation for random walks in the quenched trap model

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Abstract

We investigate subdiffusion in the quenched trap model by mapping the problem onto a new stochastic process: Brownian motion stopped at the operational time Sα=∑x=-∞(nx)α where nx is the visitation number at site x and α is a measure of the disorder. In the limit of zero temperature we recover the renormalization group solution found by Monthus. Our approach is an alternative to the renormalization group and is capable of dealing with any disorder strength.

Original languageEnglish
Article number140602
JournalPhysical Review Letters
Volume106
Issue number14
DOIs
StatePublished - 8 Apr 2011

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