Abstract: Dynamics across a Josephson junction represents a primary manifestation of quantum fluid dynamics. In the first part of this talk (i) I present a phase diagram characterizing the different dynamical regimes, and (ii) discuss underlying dissipative mechanisms across such a junction in an ultracold atomic gas: special emphasis is given on the interplay between quantum-phase-slip, acoustic emission, thermal dissipation (Bose gases) and pair-breaking (Fermi gases in BCS regime). The second part of the talk focusses on density-coupled ring-shaped atomic Bose-Einstein condensates in experimentally accessible regimes. This setting — which constitutes an alternative to tunnel-connected rings – facilitates both periodic oscillations and controllable transport of persistent currents across the two rings, the latter via a tunable weak link. Beyond dissipative effects, such process is influenced by ring geometry, external acceleration and rotation. A systematic analysis of such features allows us to propose a basic scheme for a double-ring accelerometer, discussing its operational domain, potential limitations and scheme extensions.
