Institute for Theoretical Physics • University of Cologne

Thanks to the recent impressing experimental progresses the investigation of non- equilibrium properties of driven-dissipative systems has entered the quantum world. Rydberg atoms in optical lattices, systems of trapped ions, exciton- polariton condensates, cold atoms in cavities, arrays of coupled QED cavities, are probably the most intensively investigated experimental platforms in relation to this aim. I will discuss properties of phases and phase transitions in the steady state of these systems.

The dynamics of interacting Brownian particles can be described by a stochastic  equation for the density field. I will show how the linearised version of this  equation can be used to recover, very simply, certain of Onsager's results  on electrolyte conductivity. In addition I will show how it can analyse the  out of equilibrium thermal Casimir effect between parallel plates containing  Brownian charges, in particular the case where the plates are held at different temperatures and when an electric field drives a current in one of the plates.