Fractals in the open quantum kicked top model

Fractals are one of the most important features of the classically chaotic systems. We analyze the fractal phenomena in a quantum chaos system in terms of its fidelity and dynamical localization properties in the paper. We show that, even in the open and dissipative quantum kicked top model, the fidelity displays fractal fluctuations if the underlying dynamics is in the classically chaotic regime. Moreover, the fluctuations of the inverse participation ratio which characterize the dynamical localization behavior also exhibit fractality. The relations between the fractal dimensions and the decoherence rates are explored.