2010 Fiscal Year Final Research Report
Analysis of Schrodinger operators with random δ magnetic fields
| Project/Area Number |
20740093
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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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 Kyoto Institute of Technology, 工芸科学研究科, 准教授 (90378597)
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| Research Collaborator |
NOMURA Yuji 愛媛大学, 大学院・理工学研究科, 准教授 (40282818)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 解析学 / 関数解析学 / 関数方程式論 / 数理物理 |
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| Research Abstract |
We give the range of the spectrum of the Schrodinger operators with random delta magnetic fields of the Anderson type, or of the Poisson type, and estimate the degeneracy of the Landau levels. We prove the Lifshitz tail for the Anderson case. We also study the Schrodinger operators with delta magnetic fields on the Poincare upper half plane, and estimate the number of eigenvalues in Landau gaps for finite delta fields, and the degeneracy of the Landau levels for the lattice case.
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