From Quenched Disorder to Continuous Time Random Walk

Abstract

This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to t/{\Lambda }^{1/\alpha }$ for transient process on translationally invariant lattice, in the sub-diffusive regime, is sufficient for asymptotic mapping. Exact form of the constant ${\Lambda }^{1/\alpha }$ is established. Disorder averaged position probability density function for quenched trap model is obtained and analytic expressions for the diffusion coefficient and drift are provided.

References in corpus (17)

• Langevin equations for continuous time Lévy flights
• Random walk with barriers: Diffusion restricted by permeable membranes
• Dynamics of self-propelled Janus particles in viscoelastic fluids
• Weak disorder: anomalous transport and diffusion are normal yet again
• Geometry-induced superdiffusion in driven crowded systems
• Scaling limit for trap models on ${\mathbb{Z}}^d$
• Anomalous diffusion of driven particles in supercooled liquids
• Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature
• Disentangling sources of anomalous diffusion
• Time transformation for random walks in the quenched trap model
• Time-Dependent Fluctuations and Superdiffusivity in the Driven Lattice Lorentz Gas
• Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit
• Linear and non linear response in the aging regime of the 1D trap model
• Weak subordination breaking for the quenched trap model
• Randomly trapped random walks
• Field-induced superdiffusion and dynamical heterogeneity
• Duality between random trap and barrier models

Cited by in corpus (5)

• Packets of Diffusing Particles Exhibit Universal Exponential Tails
• Transport in disordered systems: the single big jump approach
• The case of the biased quenched trap model in two dimensions with diverging mean dwell times
• Generalized master equation for first-passage problems in partitioned spaces
• The Transient Case of The Quenched Trap Model