Mathematics of disordered topological matter

无序拓扑物质的数学

• 批准号: 521509459
• 负责人: Professor Dr. Hermann Schulz-Baldes
• 金额: --
• 依托单位: Department Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/521509459?language=en
• 关键词: Mathematics; disordered; topological; matter

Topological invariants and their index theory, the bulk-boundary correspondence (BBC) and the more recently introduced spectral localizer are well-established mathematical concepts for disordered topological insulators and are also influential for numerical studies of such materials. This proposal is about extending prior results and techniques to systems with crystalline defects, disordered semimetals and topological metals, as well as non-hermitian topological systems stemming from (leaky and driven) photonics and metamaterials. Another part of the proposal aims at a deeper understanding of scattering on such topological systems.

拓扑不变量和它们的指数理论，体边界对应（BBC）和最近引入的谱定位子是无序拓扑绝缘体的成熟数学概念，也是对此类材料的数值研究有影响的。这个提议是关于将先前的结果和技术扩展到具有晶体缺陷、无序半金属和拓扑金属的系统，以及源于（泄漏和驱动）光子学和超材料的非厄米拓扑系统。该提案的另一部分旨在更深入地了解这种拓扑系统上的散射。