2013 Fiscal Year Final Research Report
Probabilistic study on the spectra of random Schroedinger operators
| Project/Area Number |
21540175
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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 | Kyoto University |
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Principal Investigator |
NAOMASA Ueki 京都大学, 人間・環境学研究科(研究院), 教授 (80211069)
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| Co-Investigator(Renkei-kenkyūsha) |
FUKUSHIMA Ryoki 京都大学, 数理解析研究所, 講師 (60527886)
TAKAHARA Jyunichi 京都大学, 大学院人間・環境学研究科, 元 研修員
KITAGAKI Yoshihiko 京都大学, 大学院人間・環境学研究科, 元 大学院生
UENO Yasufumi 京都大学, 大学院人間・環境学研究科, 大学院生
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 確率解析 / 微分方程式 / 作用素論 / 数理物理 / ランダムシュレディンガー作用素 / スペクトル / Wegner 型評価 / 磁場 |
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| Research Abstract |
One of the typical properties of the random Schroedinger operators is that the density of states decays exponentially. In our work, we reveal the transition of this behavior as the variation of the strength of the randomness and the potential. Another typical more well- known property is the Anderson localization. In our work, we extend the mathematical proof of the existence of this localization to the case that the magnetic field is a Gaussian random field, which is the most fundamental and natural random field.
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Research Products
(16 results)
