Effects of stickiness on the quantum states of strongly chaotic open systems

TL;DR

This paper explores how classical stickiness influences quantum state localization in open chaotic systems, revealing a strong correlation between classical and quantum measures and suggesting ways to control quantum state delocalization.

Contribution

It demonstrates the impact of classical stickiness on quantum state structures in open systems and links classical dwell times with quantum localization metrics.

Findings

Classical stickiness persists in strong chaos regimes.

Classical dwell time correlates with quantum dwell time and Wehrl entropy.

Knowledge of classical trajectories can guide leak placement to control quantum localization.

Abstract

We investigate the effects of classical stickiness (orbits temporarily confined to a region of the chaotic phase space) to the structures of the quantum states of an open system. We consider the standard map of the kicked rotor and verify that regions of stickiness survive in the strong chaotic regime of the closed classical map. By scanning the system's phase space with a leak, we analyze how stickiness affects the degree of localization of the states of the quantum system. We find an excellent correspondence between the classical dwell time and finite-time Lyapunov exponents with the quantum dwell time and Wehrl entropy of the quantum states. Our approach suggests that knowledge of the structure of the classically chaotic trajectories can be used to determine where to place the leak to enhance or decrease the degree of delocalization of the quantum states.