Dynamical Tunneling in Many-Dimensional Chaotic Systems

TL;DR

This paper explores how dynamical tunneling rates are significantly increased in many-dimensional chaotic systems due to Anderson transition-induced delocalization, indicating the common occurrence of amphibious states.

Contribution

It demonstrates the enhancement of tunneling rates in many-dimensional systems caused by Anderson transition, extending the understanding of amphibious states beyond one-dimensional models.

Findings

Tunneling rate is drastically enhanced at the Anderson transition.

Delocalization of chaotic states facilitates increased tunneling.

Amphibious states are likely common in many-dimensional systems.

Abstract

We investigate dynamical tunneling in many dimensional systems using a quasi-periodically modulated kicked rotor, and find that the tunneling rate from the torus to the chaotic region is drastically enhanced when the chaotic states become delocalized as a result of the Anderson transition. This result strongly suggests that amphibious states, which were discovered for a one-dimensional kicked rotor with transporting islands [L. Hufnagel et al., Phys. Rev. Lett. 89, 154101 (2002)], quite commonly appear in many dimensional systems.