Time transformation for random walks in the quenched trap model

Abstract

Diffusion in the quenched trap model is investigated with an approach we call weak subordination breaking. We map the problem onto Brownian motion and show that the operational time is ${\mathcal{S}}_{\alpha }={\sum }_{x=-\infty }^{\infty }(n_x{)}^{\alpha }$ where $n_x$ is the visitation number at site $x$ . In the limit of zero temperature we recover the renormalization group (RG) solution found by Monthus. Our approach is an alternative to RG capable of dealing with any disorder strength.

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• Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
• Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving
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• Sample-dependent first-passage time distribution in a disordered medium
• Tracer Diffusion on a Crowded Random Manhattan Lattice
• From Quenched Disorder to Continuous Time Random Walk
• The case of the biased quenched trap model in two dimensions with diverging mean dwell times
• The Transient Case of The Quenched Trap Model
• Exact Results for First-Passage-Time Statistics in Biased Quenched Trap Models