GRK 1838: Spectral Theory and Dynamics of Quantum Systems

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Science and technology are being pervaded by applications of quantum physical laws at an ever-increasing rate. Computer-aided modern drug design, medical imaging (NMR) and (radiation-) treatment, micro-electronics and photovoltaics (based on semiconductor physics) would all not exist without our knowledge of quantum physics. While the fundamental quantum mechanical laws behind these applications are well understood in terms of mathematical equations, the mathematical complexity of interacting many-particle quantum systems prevents one from connecting important quantum phenomena with the aforementioned basic laws. This is not only unsatisfactory from an academic point of view, but in the long run, it will likely hamper progress in science and technology. It therefore seems indispensable that progress on a fundamental mathematical level concerning many-body quantum systems attempts to keep pace with the developments in the applied sciences. This mathematical progress as well as the education of the next generation of experts in the mathematics of complex quantum systems is at the heart of this Research Training Group. The research programme consists of a set of mathematical projects concerning important model systems from solid-state physics and quantum electrodynamics. The specific projects address mathematical problems at the forefront of what can be done with presently available mathematical technology and their solution requires the collaboration of experts in various fields of mathematical analysis. The participating scientists from Stuttgart and Tübingen are all foremost experts in mathematical quantum mechanics and the mathematics of the Schrödinger equation. Taking advantage of the vicinity of Stuttgart and Tübingen they combine their forces into a leading centre of expertise in mathematical quantum mechanics in Germany. The Research Training Group is designed to initiate collaborations among them, to facilitate the invitation of leading scientists from abroad, and to offer a common platform for an efficient, broad and thorough education of young researchers in the mathematical analysis of many-body quantum systems.