Hybrid Schr\"odinger-Liouville and projective dynamics

Quantum dynamics provides the arguably most fundamental example of hybrid dynamics: As long as no measurement takes place, the system state is governed by the Schr"odinger-Liouville differential equation, which is however interrupted and replaced by projective dynamics at times when measurements take place. We show how this alternatingly continuous and projective evolution can be cast in form of one single differential equation for a refined state space manifold and thus be made amenable to standard port-theoretic analysis and control techniques.