Abstract

In the talk I will give an overview of our recent work on the non-equilibrium dynamics of open many-body quantum systems. These systems are described by a quantum Master equation of Lindblad form. To characterise their non-equilibrium properties we make use of the unravelling of the dynamics in terms of stochastic quantum jump trajectories. To classify dynamical phases we introduce as a dynamical order parameter the number of quantum jumps in a specific time interval. This approach rather naturally leads to a framework (called the s-ensemble) that permits an understanding of the non-equilibrium phase structure from a perspective that is very similar to that of equilibrium statistical mechanics. I will first demonstrate the approach for a driven three-level atom diplaying intermittency in its quantum jumps which is controlled by the driving fields. Then I will discuss a dissipative version of the quantum Ising model where such intermittency occurs as well but unlike in the previous case is a genuine many-body effect. Finally, I will focus on a strongly interacting many-body system with kinetic constraints that can be realised with cold excited atoms. This system displays a dynamical transition which is not accompanied by a change in the stastics. This feature results in non-trivial and strongly correlated relaxation behaviour which is reminiscent of glasses.