复合边界条件下波导中磁薛定谔算子的谱
Spectrum of the Magnetic Schrodinger Operator in a Waveguide with Combined Boundary Conditions
摘要：
我们考虑二维带中的磁薛定谔算子。在带的边界上，施加狄利克雷边界条件，除了固定段（窗口），在固定段（窗口）处，狄利克雷边界条件切换到磁诺依曼边界条件（参见第2节，方程102）。(2.2)这个边界条件的定义。我们处理一个光滑的紧支撑场以及Aharonov-Bohm场。我们给出了一个窗口的最大长度的估计，该窗口的离散谱所考虑的运营商将是空的。在紧支域的情形下，我们也给出了本征值在本质谱以下存在的一个充分条件。
英文摘要：
We consider the magnetic Schrodinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann boundary condition (see Section 2, Eq. (2.2) for the definition of this boundary condition}. We deal with a smooth compactly supported field as well as with the Aharonov-Bohm field. We give an estimate on the maximal length of the window, for which the discrete spectrum of the considered operator will be empty. In the case of a compactly supported field we also give a sufficient condition for the presence of eigenvalues below the essential spectrum.
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