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2022 Fiscal Year Final Research Report

Mathematical and experimental verification of time operators

Research Project

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Project/Area Number 20K20886
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Review Section Medium-sized Section 12:Analysis, applied mathematics, and related fields
Research InstitutionKyushu University

Principal Investigator

Hiroshima Fumio  九州大学, 数理学研究院, 教授 (00330358)

Project Period (FY) 2020-07-30 – 2023-03-31
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
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.

Free Research Field

作用素論、確率解析、場の量子論

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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Published: 2024-01-30  

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