Localization Properties of Interacting Disordered Quantum Systems

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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.