# Resonant tunneling in a system with correlated pure point spectrum

## TL;DR

This paper investigates resonant tunneling between localized states in correlated disordered systems, revealing that exponential resolvent localization does not necessarily lead to exponential dynamical localization, with implications for many-body localization models.

## Contribution

It provides new insights into the relationship between resolvent and dynamical localization in correlated disordered systems, challenging previous assumptions.

## Key findings

- Resonant tunneling occurs in systems with correlated disorder.
- Exponential resolvent localization does not imply exponential dynamical localization.
- Implications for models of many-body localization.

## Abstract

We consider resonant tunneling between disorder localized states in a potential energy displaying perfect correlations over large distances. The phenomenon described here may be of relevance to models exhibiting many-body localization. Furthermore, in the context of single particle operators, our examples demonstrate that exponential resolvent localization does not imply exponential dynamical localization for random Schr\"odinger operators with correlated potentials.