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，因为发现了与不同数学领域的联系，这些联系允许对这些模型中的相变进行严格的证明。在本提案中，我们对最近发现的一个感兴趣。与某些随机薛定谔算子的连接，这些算子用于模拟无序介质中电子的传播，我们的目标是将成熟的量子无序系统理论与这些新结果相结合，并进一步利用这些连接来研究无序量子系统中的相变。 .我们期望我们的致力于为 Sabot 和 Zeng 最近提出的问题提供至少部分答案，并以此有助于理解无序固体理论中长期存在的开放问题，即安德森金属-绝缘体转变无序的量子系统。