# Classical and quantum systems: transport due to rare events

## TL;DR

This paper reviews how rare events can facilitate energy transport in classical and quantum many-body systems, highlighting mechanisms that break localization and their potential applications.

## Contribution

It identifies and compares transport mechanisms due to rare events in classical and quantum many-body localized systems, including disorder-free and disordered models.

## Key findings

- Rare events can induce energy transport in classical systems.
- Mechanisms for transport in quantum systems are still debated.
- Potential pathways for delocalization in disordered quantum systems.

## Abstract

We review possible mechanisms for energy transfer based on 'rare' or 'non-perturbative' effects, in physical systems that present a many-body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non-quantum systems, the breakdown of localization is usually not regarded as an issue, and we thus aim at identifying the fastest channels for transport. Next, we contemplate the possibility of applying the same mechanisms in quantum systems, including disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized systems with mobility edges at energies below the edge, and strongly disordered lattice systems in $d>1$. For quantum mechanical systems, the relevance of these considerations for transport is currently a matter of debate.