Duality symmetries and effective dynamics in disordered hopping models

Abstract

We identify a duality transformation in one-dimensional hopping models that relates propagators in general disordered potentials linked by an up-down inversion of the energy landscape. This significantly generalises previous results for a duality between trap and barrier models. We use the resulting insights into the symmetries of these models to develop a real-space renormalisation scheme that can be implemented computationally and allows rather accurate prediction of propagation in these models. We also discuss the relation of this renormalisation scheme to earlier analytical treatments.

29 pages, 7 figs. Final version, some extra context and references added

References in corpus (8)

• Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary
• Subdiffusion and dynamical heterogeneities in a lattice glass model
• Non equilibrium dynamics of disordered systems : understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space
• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
• Duality between random trap and barrier models
• Subdiffusive motion in kinetically constrained models

Cited by in corpus (11)

• Topological localization in out-of-equilibrium dissipative systems
• Relationship between Entropy and Diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape
• Particle dynamics in two-dimensional random energy landscapes - experiments and simulations
• Brownian particles on rough substrates: Relation between the intermediate subdiffusion and the asymptotic long-time diffusion
• Weak subordination breaking for the quenched trap model
• A proof by graphical construction of the no-pumping theorem of stochastic pumps
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents
• Run-and-tumble particles in speckle fields
• Anomalous dimensionality dependence of diffusion in a rugged energy landscape : How pathological is one dimension ?
• Duality and fluctuation relations for statistics of currents on cyclic graphs
• Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach