Recovery of chaotic tunneling due to destruction of dynamical localization by external noise

TL;DR

This paper investigates how external noise can restore quantum tunneling suppressed by dynamical localization in chaotic systems, revealing a noise-dependent tunneling rate and its relation to localization length.

Contribution

It demonstrates that adding noise can mitigate dynamical localization effects, restoring tunneling, and establishes a scaling relation between tunneling rate, noise intensity, and localization length.

Findings

Noise attenuates dynamical localization, enhancing tunneling.

Tunneling rate scales perturbatively with noise at low intensities.

Tunneling rate saturates at high noise intensities.

Abstract

Quantum tunneling in the presence of chaos is analyzed, focusing especially on the interplay between quantum tunneling and dynamical localization. We observed flooding of potentially existing tunneling amplitude by adding noise to the chaotic sea to attenuate the destructive interference generating dynamical localization. This phenomenon is related to the nature of complex orbits describing tunneling between torus and chaotic regions. The tunneling rate is found to obey a perturbative scaling with noise intensity when the noise intensity is sufficiently small and then saturate in a large noise intensity regime. A relation between the tunneling rate and the localization length of the chaotic states is also demonstrated. It is shown that due to the competition between dynamical tunneling and dynamical localization, the tunneling rate is not a monotonically increasing function of Planck's constant. The above results are obtained for a system with a sharp border between torus and chaotic regions. The validity of the results for a system with a smoothed border is also explained.