| Project/Area Number |
19K14609
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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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 | Tokai University |
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Principal Investigator |
Iyoda Eiki 東海大学, 理学部, 講師 (50725851)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Keywords | 固有状態熱化仮説 / ゆらぎの定理 / 数値的厳密対角化 / 統計力学基礎論 / 数値計算 |
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| Outline of Research at the Start |
本研究では、孤立量子多体系における熱平衡化の数値的研究を行う。近年の研究により、可逆なユニタリ時間発展によって平衡状態への緩和が生じ得ることが実験、数値計算、理論研究によって示されてきた。熱平衡化の十分条件としては固有状態熱化仮説が有望視されている。本研究では数値計算を用いて、(1) 一般のハミルトニアン・物理量に対してETHがいつ成立するのか (2) 熱平衡化のタイムスケールがどのように決まるのかを明らかにしたい。
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| Outline of Final Research Achievements |
In order to understand relaxation and thermodynamics from quantum mechanics, we mainly studied the fluctuation theorem, which is an extension of the second law of thermodynamics in isolated quantum many-body systems, and relaxation time. The former was shown in our previous study in the short-time regime when the initial state of the heat bath is an energy eigenstate and the time evolution obeys the Schroedinger equation. In the present study, we theoretically and numerically showed that the fluctuation theorem holds also in the long-time regime. We also studied the relaxation time of physical quantities to the long-time average. We have shown that if the initial state of the heat bath is an energy eigenstate, and if the ETH of a certain time-dependent nonlocal physical quantities holds, then the relaxation time is same as that with the micro canonical heat bath.
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| Academic Significance and Societal Importance of the Research Achievements |
量子技術の発達により人工量子多体系を用いた量子シミュレータを用いた統計力学の基礎的な研究が実験的・理論的・数値的に行われるようになっている。本研究はミクロで可逆な量子力学のレベルから、マクロで不可逆な熱力学・統計力学の法則の理解を深めるための研究である。本研究で得られた知見が、今後の量子シミュレータの研究に寄与することを期待したい。
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