| Project/Area Number |
18K03467
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Seikei University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 孤立量子系 / 非平衡統計力学 / エントロピー生成 / 量子系 / 熱平衡化 |
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| Outline of Final Research Achievements |
We explored the construction of non-equilibrium statistical mechanics from an operational perspective.
First, we investigated the relaxation to steady states in isolated quantum systems in terms of weak convergence. Specifically, we showed that the relaxation to generalized Gibbs ensembles in quadratic integrable systems as mixing of local operators. We also investigated a foundation for the eigenstate thermalization hypothesis based on the uncertainty relation between energy and time. Also, we showed an inequality that provides lower bound of the entanglement entropy.
Furthermore, we derived necessary and sufficient conditions from the perspective of fluctuation theorems by extending thermodynamic uncertainty relations valid in many non-equilibrium systems to quantum systems in integrable models.
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| Academic Significance and Societal Importance of the Research Achievements |
平衡状態および平衡近傍については、統計力学による理解が進んでいる。一方、孤立量子系における熱平衡化やミクロ系における輸送現象をはじめとする非平衡現象については、急速に理解が深まりつつある。しかし、孤立量子系における熱平衡化のダイナミクスについては局所保存量の役割や緩和時間の決定要因等不明な点が多い。また、熱平衡化を受け入れることで、ミクロ系の動作原理を扱う理論として、確率的熱力学が発展しつつある。
本研究では、熱平衡化のメカニズムについて理解が進んだこと、確率的熱力学を更に発展させたことが意義深いと考えられる。
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