Quantum Breaking Time Scaling in the Superdiffusive Dynamics

We show that the breaking time of quantum-classical correspondence depends on the type of kinetics and the dominant origin of stickiness. For sticky dynamics of quantum kicked rotor, when the hierarchical set of islands corresponds to the accelerator mode, we demonstrate by simulation that the breaking time scales as ${\tau }_{\mathrm{\hslash }}\sim (1\mathrm{/}\mathrm{\hslash }{)}^{1\mathrm{/}\mu }$ with the transport exponent $\mu >1$ that corresponds to superdiffusive dynamics. We discuss also other possibilities for the breaking time scaling and transition to the logarithmic one ${\tau }_{\mathrm{\hslash }}\sim \ln (1\mathrm{/}\mathrm{\hslash })$ with respect to $\mathrm{\hslash }$.