GRK 1838: Spectral Theory and Dynamics of Quantum Systems

科学和技术正以越来越快的速度被量子物理定律的应用所渗透。如果没有量子物理学的知识，计算机辅助的现代药物设计、医学成像（核磁共振）和（辐射）治疗、微电子学和光电（基于半导体物理学）都将不复存在。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阻碍了人们将重要的量子现象与上述基本定律联系起来。这不仅从学术的角度来看是不令人满意的，而且从长远来看，它可能会阻碍科学技术的进步。因此，在涉及多体量子系统的基础数学水平上的进步，试图与应用科学的发展保持同步，似乎是必不可少的。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本研究培训小组的核心。研究计划包括一系列涉及固态物理和量子电动力学重要模型系统的数学项目。具体的项目处理的是当前可用的数学技术所能解决的最前沿的数学问题，它们的解决方案需要各个数学分析领域的专家的合作。来自斯图加特和<s:1>宾根的参与科学家都是数学量子力学和Schrödinger方程数学方面的顶尖专家。利用斯图加特和<s:1>宾根附近的优势，他们将他们的力量结合起来，成为德国数学量子力学的领先专业中心。研究培训小组旨在促进他们之间的合作，促进来自国外的顶尖科学家的邀请，并为年轻研究人员在多体量子系统的数学分析方面提供一个有效，广泛和彻底的教育的共同平台。

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.