Quenched localisation in the Bouchaud trap model with regularly varying traps

TL;DR

This paper investigates the Bouchaud trap model on integers with regularly varying traps, showing that the system exhibits both strong localization and complete delocalization at arbitrarily large times.

Contribution

It establishes the quenched localization behavior of the model, demonstrating the coexistence of localization and delocalization phenomena for almost every trapping landscape.

Findings

Existence of highly localized states at large times

Existence of completely delocalized states at large times

Localization and delocalization occur arbitrarily often

Abstract

This article describes the quenched localisation behaviour of the Bouchaud trap model on the integers with regularly varying traps. In particular, it establishes that for almost every trapping landscape there exist arbitrarily large times at which the system is highly localised on one site, and also arbitrarily large times at which the system is completely delocalised.