1995 Fiscal Year Final Research Report Summary
Study on Geometric Analysis
| Project/Area Number |
06452006
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
SUNADA Toshikazu Tohoku University Graduate School of Science Professor, 大学院理学研究科, 教授 (20022741)
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| Co-Investigator(Kenkyū-buntansha) |
UZAWA Tohru Tohoku University Graduate School of Science Associate Prof, 大学院理学研究科, 助教授 (40232813)
SAITO K. Tohoku University Graduate School of Science Associate Prof, 大学院理学研究科, 助教授 (60004397)
BANDO Shigetoshi Tohoku University Graduate School of Science Professor, 大学院理学研究科, 教授 (40165064)
NISHIKAWA Seiki Tohoku University Graduate School of Science Professor, 大学院理学研究科, 教授 (60004488)
MORITA Yasuo Tohoku University Graduate School of Science Professor, 大学院理学研究科, 教授 (20011653)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Global Analysis / Eigonvalue Problem / Quantum Ergodiuty / Oyerator Algebras |
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| Research Abstract |
1. We have found a new formulation of quantum ergodicity, and established a remarkable relationship between quantum erogodicity and classical ergodicity. A key concepts is the space average and time average in quantum mechnical systems. The method we took up is geometric analysis of pseudo differential operators and Fourier integral operators.
2. We could establish a theorem on the structure of the spectrum of discrete periodic magnetic Schroedinger operators. In particular, we found a mechanism in terms of group algebras why the band structure comes out. The second cohomology group of graph-automorphism group plays an important role. It is still interesting to investigate the relation between the spectral structure and operator algebras associated with Schroedinger operators on a graph.
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