Chaos-assisted tunneling in the presence of Anderson localization

TL;DR

This paper investigates how Anderson localization in a chaotic sea influences chaos-assisted tunneling, revealing a transition from Cauchy to log-normal tunneling rate distributions and providing a scaling theory validated by numerical models.

Contribution

It introduces a single-parameter scaling theory that describes the impact of Anderson localization on chaos-assisted tunneling rates.

Findings

Tunneling rate distribution shifts from Cauchy to log-normal with increasing localization.

The developed scaling theory accurately fits numerical data for both deterministic and disordered models.

Potential experimental setups include cold atoms, photonic lattices, and microwave billiards.

Abstract

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea. Our results show that the standard tunneling rate distribution is strongly modified by localization, going from the known Cauchy distribution in the ergodic regime to a log-normal distribution in the strongly localized case. We develop an analytical single-parameter scaling theory which accurately describes the numerical data, for both a deterministic and a disordered model. Several possible experimental implementations using cold atoms, photonic lattices or microwave billiards are discussed.