Thanks to the recent impressing experimental progresses, the investigation of non-equilibrium properties of driven-dissipative systems in quantum systems has received an impressive boost. This activity revived the study of dissipative phase transition in synthetic matter, originally started with Josephson junction arrays. Rydberg atoms in optical lattices, systems of trapped ions, exciton-polariton condensates, cold atoms in cavities, arrays of coupled QED cavities, are at present the most intensively investigated experimental platforms in relation to this aim. The predicted steady-state phase diagram of these driven dissipative systems becomes incredibly rich, displaying a variety of phenomena. I will discuss several aspects that are peculiar of these systems, not shared with the conventional picture we have at equilibrium. I will discuss in particular the possible existence of exotic phases in the steady state.

Prof. Rosario Fazio obtained his PhD degree from the University of Catania in 1989, where he became Assistant Professor in 1990 and Associate Professor in 1998. He moved in 2001 to the Scuola Normale Superiore in Pisa, and in 2005 became full Professor in SISSA, Trieste. He returned to the Scuola Normale Superiore in 2008, of which he is still Professor of Condensed Matter Physics. In 2016 he became the Head of the Condensed Matter and Statistical Physics Sector of ICTP. Currently, he is also a Visiting Professor at the Center for Quantum Technologies, National University of Singapore. His main research interests are on quantum transport in nanostructures, superconductivity (Josephson junction arrays, superconducting nanocircuits), quantum simulators (cold atoms in optical lattices, QED-arrays), non-equilibrium dynamics of many-body systems, and quantum information processing.