Focusing on the standard map of the kicked rotor, we investigate the effects of classical stickiness (orbits temporarily confined to a region of a chaotic phase space) on an open quantum system. The regions of stickiness that we identify emerge in the strongly chaotic map. By scanning the system's phase space with a leak, we show that stickiness reduces the degree of delocalization of the quantum states and the decay rate of generic initial states. We find an excellent correspondence between the classical dwell time and finite-time Lyapunov exponents with the quantum dwell time and Wehrl entropies of the quantum states. Knowledge of the structure of the classically chaotic trajectories can thus be used to determine the best placement of leaks to enhance or decrease the degree of delocalization of quantum states and to modify the quantum dynamics of open systems.

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• Chaos
• Control & applications of chaos
• Localization
• Open quantum systems
• Quantum chaos
• Quantum scars
• Quantum kicked rotor