Non-equilibrium phase transitions in open quantum systems with several absorbing states

多体系统是有趣的，因为它们可以表现出集体行为，即使在基本成分之间的相互作用是精确已知的情况下，也很难预测。集体效应的直接表现是相变，例如物质在足够低的温度下从液体到固体的转变。后者属于平衡相变的范畴。在这里，系统的状态由所谓的详细平衡条件决定，通常可以定义温度。在这种情况下，我们对相和相变的一般分类了解很多。更有趣的是所谓的非平衡相变。在这里，独特温度的概念通常不适用，详细的平衡条件被打破。这类系统的典型集合是具有吸收态的系统。这些是动力学可以进入的配置，但是一旦达到了这些配置，就不可能再逃脱了。一个例子是细菌菌落的种群动态，其中增殖和死亡竞争。一旦所有的细菌都死了，菌落就灭绝了，从这种吸收状态中恢复过来是不可能的了。在凝聚态和统计物理的背景下，吸收态过程因其能表现出新的集体行为而引起了人们的广泛关注。观察到的特征可能不属于上述平衡过程的范畴，其中液-固相变就是一个例子。更有趣的情况是，微观过程是“量子”的，因为非经典效应，如叠加和纠缠，在动力学中起作用。由于所需的计算资源呈指数增长，数值模拟变得极其苛刻，因此这种情况的研究极具挑战性。此外，分析方法还没有达到允许完全理解和分类出现的阶段和阶段转变的成熟程度。该项目旨在通过对具有两个或多个吸收态的系统进行系统研究，在我们对非平衡量子多体物理的理解上开辟新的领域。这一努力将促进数值和分析技术的发展。此外，它旨在揭示动态的集体现象，探索对称的作用，并分类非平衡相和它们之间的转变。这些结果有望对从事量子物理学、统计力学工作的科学家以及更广泛地对远离平衡的系统进行研究的科学家具有重要意义。

Many-body system are intriguing as they can exhibit collective behaviour that is very challenging to predict even when the interactions between fundamental constituents are precisely known. Direct manifestations of collective effects are phase transitions, for example the conversion of a substance from a liquid to a solid phase at low enough temperature. The latter falls into the class of equilibrium phase transitions. Here the state of the system is determined by so-called detailed balance conditions and typically a temperature can be defined. A lot is known about the general classification of phases and phase transitions in this scenario.Far more interesting are so-called non-equilibrium phase transitions. Here, the concept of a unique temperature is typically not applicable and detailed balance conditions are broken. A paradigmatic set of systems that fall into this class are ones that feature absorbing states. These are configurations that can be accessed by the dynamics, but once they have been reached an escape is no longer possible. An example is given by the population dynamics of bacterial colonies where proliferation and death compete. Once all bacteria are dead, the colony is extinct, and to come back from this absorbing state is no longer possible.In the context of condensed matter and statistical physics absorbing state processes have attracted much attention because they can show new types of collective behaviour. Observed features may fall outside the above-mentioned class of equilibrium processes of which the liquid-solid phase transition is one example. Even more interesting is the situation where the microscopic processes are “quantum” in the sense that non-classical effects such superpositions and entanglement play a part in the dynamics. Such scenario is extremely challenging to study as numerical simulations become extremely demanding due an exponential increase of the required computational resources. Moreover, analytical approaches have not reached a degree of maturity that permits to fully understand and classify emerging phases and phase transitions.This project aims at breaking new ground in our understanding of non-equilibrium quantum many-body physics by conducting a systematic study of systems with two or more absorbing states. This effort will deliver progress in the development of numerical and analytical techniques. Moreover, it aims to uncover dynamical collective phenomena, explore the role of symmetres and to classify non-equilibrium phases and transitions among them. The results are expected to be of relevance for a broad range of scientists working on quantum physics, statistical mechanics and – more broadly – conduct research on systems far from equilibrium.