2006 Fiscal Year Final Research Report Summary
Research on spectrum of random magnetic Schr {"o} dinger operators
| Project/Area Number |
17540148
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
NOMURA Yuji Tokyo Institute of Technology, Graduate school of science and engineering, Assistant Professor, 大学院理工学研究科, 助手 (40282818)
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| Project Period (FY) |
2005 – 2006
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| Keywords | random magnetic field / Schr"odinger operator / spectrum |
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| Research Abstract |
We consider the magnetic Schr"odinger operator on $mathbf{R}^2$. The magnetic field is the sum of a homogeneous magnetic field and periodically varying pointlike magnetic fields on a lattice. We shall give a sufficient condition for each Landau level to be an infinitely degenerated eigenvalue. This condition is also necessary for the lowest Landau level. In the threshold case, we see that the spectrum near the lowest Landau level is purely absolutely continuous. Moreover, we shall give an estimate for the density of states for Landau levels and their gaps. The proof is based on the method of Geyler and v Sv tov'iv cek, the magnetic Bloch theory, and canonical commutation relations.
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