An interesting class of open quantum systems is defined by the so-called repeated interaction scheme, where the system interacts sequentially with small and fresh subsystems or units coming from the reservoir. The interaction is unitary and relatively easy to analyze. However, it must be switched on and off, and this action introduces or extracts energy in many cases of interest, performing work and preventing thermalization. As a consequence, the repeated interaction scheme cannot be used to model thermostats in quantum thermodynamics.
We tried to overcome this problem by considering collisional reservoirs, where the units are particles that collide with the system, inducing a sudden change described by a CPTP map. For this picture to work, however, one needs to bombard the system with wave packets of finite width, and, surprisingly, this finite width can keep and even generate coherences in the system. These results prompt a fundamental question for quantum thermodynamics: what comes out by effusion from a container with a quantum gas in thermal equilibrium: waves or particles?