From a theoretical point of view treating systems that are out of equilibrium (OEQ), is one of the most difficult challenges of quantum many body physics.
Recently cold atomic systems have provided remarkable realizations of such situations. I will discuss one particular case, namely the transport of particle or charge current between two fermionic reservoirs, with controlled interactions.
A first case is the transport through a zero dimensional structure (quantum point contact) for which a full non-equilibrium solution, going beyond linear response, is needed, and for which the full current-voltage characteristics gives direct information on the physics of the problem. It allows in particular to test for the physics of multiple Andreev reflections.
The second recent experiment deals with the transport through a periodic one dimensional structure with a periodic potential. I will discuss how this allows to test for a special state of matter existing in interacting one dimensional quantum systems, the so-called Luther-Emery liquid, predicted about 40 years ago but which could not be evidenced in a controlled way in a condensed matter context.