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Gap resonance in the classical dynamics of the current-biased Josephson tunnel junctions

This work reports a novel time-domain expression for the current-response kernels of a Josephson tunnel junction between BCS superconductors with in general different energy gaps, and its use to simulate the classical dynamics of such junctions. The simulations show a dynamic regime characterized by the resonance between the Josephson oscillations and the gap oscillations in the asymptotics of the current kernels that has not been studied previously. The resonance manifests itself as a hysteresis in the dc current-voltage characteristics of the current-biased junctions in the voltage range above the energy gap, in addition to the usual ``inertial'' hysteresis characteristic for tunnel junctions at voltages below the energy gap. Features of the IV curves related to the gap resonance, including the above-the-gap hysteresis, should manifest themselves in many structures and devices utilizing high-quality Josephson tunnel junctions with relatively large, but achievable current densities.