Coulomb blockade and remnants of chaos in dissipative quantum tunnel junctions

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.