GRK 1838: Spectral Theory and Dynamics of Quantum Systems

量子物理定律的应用正以越来越快的速度渗透到科学和技术中。计算机辅助的现代药物设计，医学成像（NMR）和（辐射）治疗，微电子学和光化学（基于半导体物理学）都不会存在，如果没有我们的量子物理学知识。虽然这些应用背后的基本量子力学定律在数学方程方面得到了很好的理解，但相互作用的多粒子量子系统的数学复杂性使人们无法将重要的量子现象与上述基本定律联系起来。这不仅从学术角度来看是不令人满意的，而且从长远来看，它可能会阻碍科学和技术的进步。因此，在多体量子系统的基本数学水平上的进展，似乎必须努力跟上应用科学的发展。这种数学进步以及下一代复杂量子系统数学专家的教育是这个研究培训小组的核心。该研究计划包括一套关于固态物理学和量子电动力学的重要模型系统的数学项目。具体的项目解决的数学问题的最前沿可以做什么与目前可用的数学技术和他们的解决方案需要在数学分析的各个领域的专家的合作。来自斯图加特和图宾根的参与科学家都是数学量子力学和薛定谔方程数学方面的最重要专家。利用附近的斯图加特和蒂宾根，他们联合收割机他们的力量成为一个领先的中心的专业知识，在数学量子力学在德国。研究培训小组旨在启动他们之间的合作，促进邀请国外领先的科学家，并提供一个共同的平台，为年轻研究人员提供多体量子系统数学分析方面的有效，广泛和全面的教育。

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.