Landau levels on the hyperbolic plane in the presence of Aharonov-Bohm fields

被引：2

作者：

Mine, Takuya ^{[1
]}

Nomura, Yuji ^{[2
]}

机构：

[1] Kyoto Inst Technol, Grad Sch Sci & Technol, Sakyo Ku, Kyoto 6068585, Japan

[2] Ehime Univ, Dept Comp Sci, Grad Sch Sci & Engn, Matsuyama, Ehime 7908577, Japan

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 263卷 / 06期

关键词：

Magnetic Schrodinger operator; Landau level; Zero-mode; Pauli operator; Hyperbolic plane; Aharonov-Bohm effect; Aharonov-Casher theorem; EIGEN-VALUE-PROBLEM; SCHRODINGER-OPERATORS; AUTOMORPHIC-FORMS; ZERO MODES; SPECTRAL PROPERTIES; MAGNETIC-FIELDS; PAULI OPERATOR; GROUND-STATES; RESOLVENT; SOLENOIDS;

D O I：

10.1016/j.jfa.2012.06.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the magnetic Schrodinger operators on the Poincare 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 delta 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. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1701 / 1743

页数：43

共 39 条

[1] On the Aharonov-Bohm Hamiltonian [J].