Coulomb blockade and remnants of chaos in dissipative quantum tunnel junctions

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Abstract
Dissipation is important for many systems whose behavior lies between classical and quantum physics. Such systems are of interest to test ideas about quantum chaos; yet there is no suitable formulation of dissipative quantum mechanics for computing dynamics. This paper describes our effort to formulate and solve numerically one such system, the small-area tunnel junction, with or without superconducting electrodes. We take a phenomenological approach using a damping term in a washboard Hamiltonian. For dc bias, the simulations give the Josephson effect or the Coulomb blockade in the appropriate limits. We also apply a sinusoidal current bias to the junction, using parameters that would give chaos in the corresponding classical equations of motion. In this case, the quantum dynamics has a classical remnant in the form of long chaotic transients at the classical boundary of chaos. However, the quantum system eventually becomes periodic for all parameters tried so far.