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，由于与不同数学领域的联系，加强的随机过程引起了科学界的极大兴趣，这些连接允许在这些模型中进行严格的相换事证明。在此提案中，我们对最近发现的某些随机Schrödinger操作员的联系感兴趣，这些连接用于模拟无序介质中电子的传播。我们的目标是将量子混乱系统的良好发展理论与这些新结果相结合，并进一步探索这些连接，以研究无序量子系统中的相变。我们希望我们的工作至少为Sabot和Zeng提出的最新问题提供部分答案，并因此有助于理解无序固体理论中长期存在的开放问题，即Anderson Metal-Metal-Metal-Metal-Metal-Munduntator to Anderson Metal-Metal-Mentum-undustrator for dise量子系统。