Random Schrödinger operators arising in the studyof reinforced random processes

强化随机过程研究中出现的随机薛定谔算子

• 批准号: 417891127
• 负责人: Professorin Dr. Margherita Disertori, since 9/2019
• 金额: --
• 依托单位: Institut für Angewandte Mathematik (IAM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/417891127?language=en
• 关键词: Random; Schr; dinger; operators; arising

In recent years, reinforced random processes have attracted much interest from the scientific community due to the discovery of connections with different areas of mathematics that have allowed for rigorous proofs of phase transitions in these models. In this proposal, we are interested in a recently discovered connection with certain random Schrödinger operators, which are used to model the propagation of electrons in disordered media. Our goal is to combine the well developed theory of quantum disordered systems with these new results and exploit these connections further to study phase transitions in disordered quantum systems. We expect our work to provide at least a partial answer to a recent question formulated by Sabot and Zeng, and with this, to contribute to the understanding of a long-standing open problem in the theory of disordered solids, namely, the Anderson metal-insulator transition for disordered quantum systems.

近年来，强化随机过程引起了科学界的极大兴趣，这是由于发现了与不同数学领域的联系，这些数学领域允许在这些模型中严格证明相变。在这个提议中，我们感兴趣的是最近发现的与某些随机薛定谔算子的联系，这些算子用于模拟电子在无序介质中的传播。我们的目标是联合收割机的量子无序系统的良好发展的理论与这些新的结果，并利用这些连接进一步研究无序量子系统中的相变。我们希望我们的工作至少能部分回答Sabot和Zeng最近提出的一个问题，并以此为基础，有助于理解无序固体理论中一个长期悬而未决的问题，即无序量子系统的安德森金属-绝缘体转变。