| Project/Area Number |
26400145
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Gakushuin University |
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Principal Investigator |
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| Research Collaborator |
Minami Nariyuki
Ueki Naomasa
Sadahiro Taizo
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 準位統計 / ランダム行列理論 / サインベータ過程 / ポアソン過程 / ランダムシュレーディンガー作用素 / 固有関数 / ガウシアンベータアンサンブル / ガウシアンβアンサンブル / １次元拡散過程 / １次元ランダムシュレーディンガー作用素 / 南評価 / ウェグナー評価 / 点過程 |
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| Outline of Final Research Achievements |
We studied the one dimensional random Schroedinger operators with decaying facto, and with decaying coupling constant, in the order of -alpha at infinity, and our results are as follows.
(i) the level statistics are : Clock, Sine_{\beta}, and Poisson processes, depending on \alpha is bigger than, equal to, and less than 1/2, (ii) the asymptotic expansion of the number of eigenvalues on a given interval, which shows different behavior depending on the value of alpha, (iii) as a related question, the level statistics of the Gaussian beta ensemble at high temperature is Poisson.
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| Academic Significance and Societal Importance of the Research Achievements |
１次元での様々なランダムシュレーディンガー作用素において、その準位統計を考え、それがポアソン過程以外になるものを得たこと、またランダム行列理論との関係を具体的に示したこと。またランダムシュレーディンガー作用素の研究手法のランダム行列理論への応用例。
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