论文标题
无界Dirac-Landau运营商的散装通信
Bulk-edge correspondence for unbounded Dirac-Landau operators
论文作者
论文摘要
我们考虑在整个平面上定义的二维无界磁性狄拉克运算符，或在半平面上使用无限的质量边界条件。我们的主要结果使用了椭圆PDES和积分算子的技术，而其拓扑后果则作为一些更一般身份的推论，涉及大体和边缘运算符的快速衰减功能的局部轨迹的磁性导数。这些真相之一会导致所谓的st找法公式：如果散装操作员具有孤立的紧凑型光谱岛，那么相应的散装光谱投影的整合密度与磁场的差异变化，只要光谱岛和光谱的其余部分都不会封闭，并构成了chern variiifict of the Spectrum之间的差异。相同的散装Chern角色与出现在散装操作员差距中的边缘状态的数量有关。
We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane, or with infinite mass boundary conditions on a half-plane. Our main results use techniques from elliptic PDEs and integral operators, while their topological consequences are presented as corollaries of some more general identities involving magnetic derivatives of local traces of fast decaying functions of the bulk and edge operators. One of these corollaries leads to the so-called Středa formula: if the bulk operator has an isolated compact spectral island, then the integrated density of states of the corresponding bulk spectral projection varies linearly with the magnetic field as long as the gaps between the spectral island and the rest of the spectrum are not closed, and the slope of this variation is given by the Chern character of the projection. The same bulk Chern character is related to the number of edge states which appear in the gaps of the bulk operator.
