Non-equilibrium phase transitions

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Phase transitions rank among the most fascinating phenomena of statistical physics. Argua-bly they constitute the conceptually cleanest and most prominent example of the general phenomena that an interacting systems can behave significantly different than its parts; a concept known as emergence. Understanding phase transitions has thus attracted a great deal of research interest throughout the last century. By now, we are using the knowledge steaming from this research in every days life, such as, e.g., in classical antifreeze sub-stances. Especially, fascinating are the phase transitions found in quantum systems, as they often defy our intuition. Exploring phase transitions in those quantum systems had an immense impact on applications, leading to the development of, e.g,. phase change materials (for heating or cooling), phase change memories (for alternative computing and data storage solutions) or superconductors (to eliminate electrical resistance). On a theoretical level phase transitions in strongly correlated quantum system pose a formidable task, even after powerful tools, such as the Ginsburg-Landau approach and the renormalization group theory, have been developed. Thus even today phase transitions in those systems are an active field of research. The description of phase transitions has focused mainly on equilibrium, but recently controlled experimental realizations of non-equilibrium quantum many-body systems were devised as well. Those experimental systems rank from the prominent ultra-cold gases, to semiconductor quantum dot setups or pump-probe experiments in metals and insulators, which all excel in the precise manipulation of the different systems at hand. Therefore, non-equilibrium has increasingly shifted into the focus of research attention. Within this project we want to describe the combination of the physics of phase transitions and non-equilibrium. New phases of matter were reported as systems were put out of their equilibrium state. Some of those novel phases are inaccessible by the pathways of equilibrium and were consequently dubbed hidden phases. We aim at a more complete understanding of these non-equilibrium phases in quantum many-body systems and of the mechanism, which drive the transition from one phase to the other. We want to achieve this by a bottom-up approach, studying quantum many-body systems of successively increasing complexity. Understanding the non-equilibrium phases in these systems will hopefully lead to interesting applications, as new (hidden) phases can easily be controlled by the external fields, driving the system away from equilibrium.