2013 Fiscal Year Final Research Report
Analysis on Schroedinger operators with delta-like magnetic fields on Riemannian manifolds
| Project/Area Number |
23740122
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Kyoto Institute of Technology |
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Principal Investigator |
MINE Takuya 京都工芸繊維大学, 工芸科学研究科, 准教授 (90378597)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 数理物理 / 関数方程式 / 関数解析学 / シュレディンガー方程式 / アハラノフ・ボーム効果 / 量子力学 |
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| Research Abstract |
The Aharonov-Bohm effect is known as an observable quantum effect by the magnetic vector potential, which is introduced in the classical electrodynamics only as a computational tool. In this subject, we study the effect of the Aharonov-Bohm magnetic fields (delta-like magnetic fields) on the spectrum of the Schroedinger operators on Riemannian manifolds. Especially, we consider the Schroedinger operators on the hyperbolic plane with a constant magnetic field plus the Aharonov-Bohm magnetic fields placed periodically on a hyperbolic lattice, and study the threshold value of the magnetic fluxes for the existence of the infinitely degenerated Landau levels. Moreover, we consider the Schroedinger operators on the Euclidean plane with two quantized Aharonov-Bohm magnetic fields, and give an explicit form of the eigenfunctions in terms of the Mathieu functions.
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