论文标题
拓扑边缘状态的恢复状态
Cobordism invariance of topological edge-following states
论文作者
论文摘要
我们证明，每当哈密顿操作员在压缩到具有边界的域时遇到粗糙的指数阻塞时，光谱缝隙填充现象就会发生。此外，间隙填充光谱有助于量化的电流通道，后者随后并定位在可能复杂的边界处。该指数障碍物表明对域边界的变形不敏感，因此该现象是对磁性laplacians建模量子厅系统和Chern拓扑绝缘子的通用。一个关键的结构是ROE当地紧凑型传播操作员的代数的准等级版本。
We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current channels, which follow and are localised at the possibly complicated boundary. This index obstruction is shown to be insensitive to deformations of the domain boundary, so the phenomenon is generic for magnetic Laplacians modelling quantum Hall systems and Chern topological insulators. A key construction is a quasi-equivariant version of Roe's algebra of locally compact finite propagation operators.
