Recent experimental developments in diverse areas - ranging from cold atomic
gases over light-driven semiconductors to microcavity arrays - move systems
into the focus, which are located on the interface of quantum optics, many-body
physics and statistical mechanics. They share in common that coherent and
driven-dissipative quantum dynamics occur on an equal footing, creating genuine
non-equilibrium scenarios without immediate counterpart in condensed matter.
This concerns both their non-thermal flux equilibrium states, as well as their
many-body time evolution. It is a challenge to theory to identify novel
instances of universal emergent macroscopic phenomena, which are tied
unambiguously and in an observable way to the microscopic drive conditions. In
this review, we discuss some recent results in this direction. Moreover, we
provide a systematic introduction to the open system Keldysh functional
integral approach, which is the proper technical tool to accomplish a merger of
quantum optics and many-body physics, and leverages the power of modern quantum
field theory to driven open quantum systems.Comment: 73 pages, 13 figure
