Open quantum systems with delayed feedback

We consider models of open quantum systems in which the system couples to the reservoir at two spatial locations, effecting a feedback loop. In particular, we consider two different models for the interaction of a harmonic oscillator with a feedback reservoir: one with the standard quantum-optical approximations, and one without. The former approach yields the surprising result that damping of the oscillator can be partially or fully suppressed in certain parameter regimes, but in the latter case the situation is more complicated.