Charge-phase quantization proved to be a simple yet powerful principle to describe the dynamics of superconducting circuits within a Hamiltonian framework. However, recent developments (revolving mainly around geometric and topological properties of quantum transport) revealed significant cracks in the facade. In a series of works, we realized that one of the most important ingredients that was not accurately taken into account is the electro-motive force. In this talk, I first provide a pedagogical introduction into the current state of the art formulation of quantum circuit theory. I then show step by step why and how we need to go beyond existing principles to correctly describe time-dependent flux driving. I then explain that for regular circuits, the fundamental physical picture of a flux-driven circuit changes drastically. Already for a dc SQUID our new treatment reveals the possibility of negative or time-dependent junction capacitances, leading to strong deviations in the predictions of qubit relaxation times, and the existence of Berry curvatures with single loop drive. Finally, we turn our attention to Majorana-based circuits, where we unravel that the electro-motive force gives rise to a strong dynamical rescaling of the relevant energy scales. As a consequence, we predict frequency-dependent transitions between regimes of fractional versus integer Josephson effects.
Coffee and pastries will be served at 11:00 in the hall.