Non-equilibrium phase transitions

相变是统计物理学中最迷人的现象之一。可以说，它们构成了概念上最清晰和最突出的一般现象的例子，即相互作用的系统可以表现出与其部分显著不同的行为；这个概念被称为涌现。因此，理解相变在上个世纪吸引了大量的研究兴趣。到目前为止，我们正在日常生活中使用从这项研究中获得的知识，例如，经典的防冻物质。尤其令人着迷的是在量子系统中发现的相变，因为它们经常违背我们的直觉。在这些量子系统中探索相变对应用产生了巨大的影响，导致了诸如。相变材料（用于加热或冷却），相变存储器（用于替代计算和数据存储解决方案）或超导体（消除电阻）。在理论层面上，强相关量子系统的相变是一项艰巨的任务，即使在强大的工具，如金斯堡-朗道方法和重整化群论，已经发展。因此，即使在今天，这些系统中的相变也是一个活跃的研究领域。相变的描述主要集中在平衡态，但最近也设计了非平衡态量子多体系统的受控实验实现。这些实验系统从著名的超冷气体，到半导体量子点装置或金属和绝缘体中的泵探实验，它们都擅长于精确操纵手头的不同系统。因此，非均衡日益成为研究的焦点。在这个项目中，我们想要描述相变和非平衡物理的结合。当系统脱离平衡状态时，物质的新相被报道出来。其中一些新相无法通过平衡路径到达，因此被称为隐藏相。我们的目标是更全面地了解量子多体系统中的这些非平衡相以及驱动从一个相过渡到另一个相的机制。我们希望通过自下而上的方法来实现这一目标，研究复杂性不断增加的量子多体系统。了解这些系统中的非平衡相将有望带来有趣的应用，因为新的（隐藏的）相可以很容易地由外部场控制，使系统远离平衡。

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.