1997 Fiscal Year Final Research Report Summary
STUDY ON QUANTUM ERGODIC THEORY
| Project/Area Number |
08640079
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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 |
Geometry
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
SUNADA Toshikazu TOHOKU UNIVERSITY,MATHEMATICS,PROFESSOR, 大学院・理学研究科, 教授 (20022741)
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| Co-Investigator(Kenkyū-buntansha) |
KUROKI Gen TOHOKU UNIVERSITY,MATHEMATICS,ASSISTANT, 大学院・理学研究科, 助手 (10234593)
HASEGAWA Koji TOHOKU UNIVERSITY,MATHEMATICS,LECTURER., 大学院・理学研究科, 講師 (30208483)
NAYATANI Shin TOHOKU UNIVERSITY,MATHEMATICS,ASSOC.PROF., 大学院・理学研究科, 助教授 (70222180)
SAITO Kazuyuki TOHOKU UNIVERSITY,MATHEMATICS,ASSOC.PROF., 大学院・理学研究科, 助教授 (60004397)
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| Project Period (FY) |
1996 – 1997
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| Keywords | ERGODICITY / SPECTRUM / EIGENVALUES / QUANTUM ERGODICITY |
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| Research Abstract |
We introduced the notion of ergodicity at infinite energy level in both quantum and classical mechanics. The notion allows us to give a necessary and sufficient condition in terms of microlocal properties of eigenfunctions of a quantum hamiltonian such that the corresponding classical dynamical system is ergodic. Especially, a new insight into quantum ergodicity due to Snirelman, Zelditch and Colin de Verdiere was given.
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