2022 Fiscal Year Final Research Report
Mathematical and experimental verification of time operators
| Project/Area Number |
20K20886
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| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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| Allocation Type | Multi-year Fund |
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| Review Section |
Medium-sized Section 12:Analysis, applied mathematics, and related fields
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2020-07-30 – 2023-03-31
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| Keywords | 強時間作用素 / 弱ワイル関係 / 不確定性原理 / 正準交換関係 |
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| Outline of Final Research Achievements |
This research is an experimental verification and theoretical study of the existence of the so-called "time operators". Let H be the Hamiltonian of the system. T is called a strong time operator iff there exists a pair (H,T) satisfying the weak Weil relation. This study is an extremely challenging research to experimentally confirm the existence of time operators, which is a concept in pure mathematics. Although the research did not proceed as originally planned due to COVID 2019, we were able to hold a workshop on the time operator, publish lecture notes, and present our results both in Japan and abroad. We also verified Arai's inequality in simulations.
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| Free Research Field |
作用素論、確率解析、場の量子論
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| Academic Significance and Societal Importance of the Research Achievements |
時間作用素はハミルトニアンに付随した概念として与えられる. 数学的には時間作用素は線型作用素の一つである. 時間作用素が量子力学に関連しているため, 直接的な社会的意義はないが, 量子力学は現代科学の基礎であり, 多くの応用分野に影響を与えていることを考えれば, 社会的な進歩や技術の向上につながることがあり得る.
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