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

In strongly chaotic systems, phase space is often considered structureless. However, we reveal the existence of regions of stickiness (dynamical traps within phase space), that significantly affect the dynamics of both classical and quantum open systems. Unlike quantum scars, which have measure zero, stickiness extends over parts of the phase space. We show that stickiness reduces the overall delocalization of quantum states and the decay rate of generic initial states. The analysis is done for the classical and quantum kicked rotor with a leak. We observe a strong correspondence between the classical dwell times and finite-time Lyapunov exponents with the quantum dwell times and Wehrl entropies of the quantum states. Our study demonstrates that the position of the leak can be adjusted to control the degree of delocalization of quantum states and to modify the quantum dynamics of open systems.