论文标题
Landau操作员在螺旋表面上的分离光谱
Delocalized spectra of Landau operators on helical surfaces
论文作者
论文摘要
在平坦的表面上，Landau操作员或Hamiltonian的量子厅具有无限归化的Landau水平。我们认为远离可能的非紧凑型亚策略的表面是渐近恒定的曲率，这是我们的主要例子。如果在适当的希尔伯特模块中考虑了远离submanifold的表面的ROE代数上的适当的希尔伯特模块中的频谱，则兰道水平保持孤立。然后可以将DELACALIZER的粗糙指数分配给它们。作为应用程序，我们证明螺旋表面上的Landau操作员没有高于最低Landau水平的光谱差距。
On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely degenerate Landau levels. We consider surfaces with asymptotically constant curvature away from a possibly non-compact submanifold, the helicoid being our main example. The Landau levels remain isolated, provided the spectrum is considered in an appropriate Hilbert module over the Roe algebra of the surface delocalized away from the submanifold. Delocalized coarse indices may then be assigned to them. As an application, we prove that Landau operators on helical surfaces have no spectral gaps above the lowest Landau level.
