Duality symmetries and effective dynamics in disordered hopping models

TL;DR

This paper uncovers a duality in disordered one-dimensional hopping models, enabling a new renormalisation scheme for predicting particle propagation and extending previous trap-barrier dualities.

Contribution

It introduces a novel duality transformation for disordered hopping models and develops a computationally feasible real-space renormalisation method.

Findings

Duality relates propagators in inverted energy landscapes.

The renormalisation scheme accurately predicts propagation.

The approach generalises previous trap-barrier dualities.

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.