Landau levels on the hyperbolic plane in the presence of Aharonov–Bohm fields
Landau levels on the hyperbolic plane in the presence of Aharonov–Bohm fields
复制标题
存在阿哈罗诺夫-玻姆场时双曲平面上的朗道能级
DOI：
10.1016/j.jfa.2012.06.002
复制
发表时间：
2012
影响因子：
1.7
通讯作者：
Yuji Nomura
中科院分区：
文献类型：
--
作者：
T. Mine;Yuji Nomura
我们考虑了Poincaré上半平面上具有常高斯曲率−1的磁性薛定谔算子。我们假设磁场是由一个恒定场和放置在某个晶格上的Diracδ测度之和给出的。给出了每个Landau能级是无穷退化本征值的一个充分条件。如果上述条件成立，我们还证明了最低朗道能级不是本征值。特别地，最低朗道能级的无限简并等价于二维泡利算符零模的无穷大。
We consider the magnetic Schrödinger operators on the Poincaré upper half plane with constant Gaussian curvature −1. We assume the magnetic field is given by the sum of a constant field and the Dirac δ measures placed on some lattice. We give a sufficient condition for each Landau level to be an infinitely degenerated eigenvalue. We also prove the lowest Landau level is not an eigenvalue if the above condition fails. In particular, the infinite degeneracy of the lowest Landau level is equivalent to the infiniteness of the zero-modes of the two-dimensional Pauli operator.