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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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2021: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2020: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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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 / 時間作用素 / ワイル関係式 / 調和振動子 / 対称作用素 / ユニタリー群 / ワイルの関係式 |
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| Outline of Research at the Start |
エネルギーハミルトニアンと正準交換関係交換関係を満たす作用素である時間作用素の存在を実験的に検証する.
1. 丹田と中津川が実験を担当.
2. 廣島が数学的な部分の解析を担当
廣島は実験の進捗状況を適宜確認し, 理論的なバックアップを実験グループの丹田, 中津川に示す.
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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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| 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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Report
(4 results)
Research Products
(13 results)
