Numerical study on thermalization in isolated quantum many-body systems

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K14609
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Tokai University
• Principal Investigator: Iyoda Eiki 東海大学, 理学部, 講師 (50725851)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: 固有状態熱化仮説 / ゆらぎの定理

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.

Free Research Field

統計力学

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。