AI 中文总结
研究二维晶格哈密顿量和磁薛定谔算子在迁移率隙中的边缘谱，证明非零体拓扑指标保证整个区间属于半空间算子的绝对连续谱，且谱重数有下界。
AI 中文摘要
我们研究了二维晶格哈密顿量和磁薛定谔算子在迁移率隙中的边缘谱，迁移率隙是一个能量区间，其中体谱可能是局域的，而非必然缺失。在合适的局域化和边界假设下，我们证明了一个非零的常数体拓扑指标意味着整个区间属于相应半空间算子的绝对连续谱。在该区间内几乎每个能量处，绝对连续谱的重数都以下界由指标的绝对值所限定。第2.3节中辅助空间切割构造的初版由ChatGPT 6生成。
英文摘要
We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentially localized rather than necessarily absent. Under suitable localization and boundary assumptions, we prove that a constant nonzero bulk topological index implies that the entire interval belongs to the absolutely continuous spectrum of the corresponding half-space operator. The absolutely continuous spectral multiplicity is bounded below by the absolute value of the index at almost every energy in the interval. The first version of the auxiliary-space cut construction in Section 2.3 was generated using ChatGPT 6.
