Level repulsion in power spectra of chaotic Josephson junctions

We consider an ultrasmall Josephson junction driven by a classical time-periodic current. The whole system is isolated and free of dissipation. Charge quantization of Cooper pairs on the junction capacitor requires the quantization of the system, otherwise described by classical pendulum equations. Our investigations of the Floquet operator show that under certain conditions level repulsion of those quasienergies occurs that corresponds to the chaotic classical regime. This leads to a decrease of the spectral density in the low-frequency region constituting a quantum effect related to classical chaos.