The project aims to describe non-equilibrium dynamics in quantum field theories. The main framework is provided by quantum quenches, i.e. sudden changes in the parameters of the Hamiltonian that take the system out of equilibrium and initiate a time evolution. The general expectation in quantum statistical physics is that most systems thermalise; however, there exists a class of systems called integrable for which the existence of an infinite number of local conservation laws prevent thermalisation. The relevant questions are the following:

• Does the system reach an equilibrium which can be described by a statistical ensemble, and if yes, what is the nature of the equilibrium ensemble?
• What is the difference between integrable and non-integrable case, both regarding the stationary state and the time evolution?
• Are there any universal features of the non-equilibrium dynamics, especially regarding the propagation of correlations and the generation of entanglement?
• How does relaxation happen (if indeed it happens at all) and what are the relevant time scales?
• What is the effect of integrability breaking?

Recent scientific research has made substantial progress in these directions but there are many more open questions than final answers, and our aim is to further our understanding of the above problems. The class of systems considered consists of quantum field theories in one spatial dimensions, for which very powerful analytic and numerical approaches are available, and at the same time are relevant to strongly-correlated quantum systems that are realised in experiments.