Accelerator-mode islands and superdiffusion in double-kicked rotor

This paper presents a theoretical investigation of the presence of acceleration islands in the phase space of double-kicked rotor (DKR) systems, which can lead to superdiffusive behavior. We establish the conditions for the existence of period-1 acceleration centers and subsequently calculate the stability conditions for both period-1 and period-2 accelerate mode islands. A detailed analysis of local and global diffusion in the vicinity of the islands and the stickiness regions is provided. It is demonstrated that the mean stickiness time decays exponentially when the phase point is located in the interior of the island. Moreover, the phase point undergoes a power-law decay with a power equal to approximately 5 when entering the sticky region. These findings offer a foundation for future exploration of quantum dynamics in the DKR system.

Automated summary

This paper presents a theoretical investigation into the existence of acceleration islands in the phase space of double-kicked rotor (DKR) systems, which can result in superdiffusive behavior. The conditions for the existence of period-1 acceleration centers are established, and the stability conditions for both period-1 and period-2 accelerate mode islands are subsequently calculated. A detailed analysis of local and global diffusion in the vicinity of the islands and the stickiness regions is provided. These findings offer a foundation for future exploration of quantum dynamics in the DKR system.