Localization Properties of Interacting Disordered Quantum Systems

将进行研究，以严格理解无序对相互作用的多体量子系统的影响。人们最感兴趣的是无序材料的电子传输和导电性问题。在将要研究的模型中，将特别关注随机量子自旋系统。它们在统计物理学中经常被用作相互作用的粒子系统的模型，但在量子信息理论中也是相关的，在量子信息论中，它们描述了相互作用的量子比特。这项研究将把安德森模型等单粒子模型理论中的方法与量子自旋系统理论的最新进展相结合，如改进的Lieb-Robinson界限和基态关联的衰变特性。现代纳米技术旨在制造越来越小的强大电子器件。因此，量子效应发挥着越来越重要的作用，最初在理论物理中开发的数学模型具有越来越多的实用意义，例如在量子计算中。量子器件的物理性质受到杂质和无序效应的强烈影响，就像半导体、合金和非晶态材料中存在的那样。特别是，无序对电导率有很大的影响。这项研究的目标是帮助理解量子系统无序效应的数学原因。特别是，我们将研究无序对相互作用电子大系统的影响。工作将包括在这一研究领域培训几名博士生。

Research will be carried out to rigorously understand the effects of disorder on interacting many-body quantum systems. Of central interest are questions of electron transport and conductivity properties of disordered materials. Among models to be studied, particular attention will be given to random quantum spin systems. These are frequently used in statistical physics as models of interacting particle systems, but are also relevant in quantum information theory, where they describe interacting quantum bits. The research will combine methods from the theory of single-particle models such as the Anderson model with recent progress in the theory of quantum spin systems, such as improved Lieb-Robinson bounds and decay properties of ground state correlations.Modern nanotechnology aims at building powerful electronic devices of smaller and smaller size. As a result, quantum effects play an increasingly important role and mathematical models originally developed in theoretical physics have increasing practical relevance such as, for example, in quantum computing. The physical properties of quantum devices are strongly influenced by effects of impurities and disorder, as present in semi-conductors, alloys and amorphous materials. In particular, disorder has a strong effect on electrical conductivity. It is the goal of this research project to contribute to the understanding of the mathematical reasons for disorder effects on quantum systems. In particular, we will study the effect of disorder on large systems of interacting electrons. Work will include the training of several PhD students in this area of research.