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2023 Fiscal Year Final Research Report

Toward experimental realization of importance sampling for measuring large deviations of non-equilibrium interface fluctuations

Research Project

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Project/Area Number 20H01826
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
Research InstitutionThe University of Tokyo

Principal Investigator

Takeuchi Kazumasa  東京大学, 大学院理学系研究科(理学部), 准教授 (50622304)

Project Period (FY) 2020-04-01 – 2024-03-31
Keywords大偏差 / KPZ普遍クラス / 界面ゆらぎ / ランダム成長過程 / 確率的粒子輸送 / 重点サンプリング法 / 液晶乱流 / トポロジカル欠陥
Outline of Final Research Achievements

To develop an experimental method to study large deviations of non-equilibrium interface fluctuations in the Kardar-Parisi-Zhang (KPZ) universality class, we focused on a version of the numerical scheme called the importance sampling and adapted it to our experimental system. First we tested the validity of the method numerically, by applying it to a solvable model and comparing with exact solutions. We also developed an experimental technique to generate arbitrary initial conditions with randomness in our target system based on liquid-crystal turbulence and marked steps toward real-time analysis of microscope images. We also studied microscopic elementary processes that result in the growth process of interest macroscopically, namely dynamics of topological defect lines, using a relaxation process from the turbulent state.

Free Research Field

非平衡統計力学

Academic Significance and Societal Importance of the Research Achievements

稀にしか起こらないが重要な現象は、災害など自然現象のほか、経済活動や社会現象にも見られ、統計的性質の理解は大きな学術的・社会的意義を有する。こうした大偏差の研究は、稀な事象であるがゆえに、実験研究は極めて困難である。本研究成果は、非平衡界面ゆらぎを舞台に、従来不可能であった大偏差の実験研究の端緒を開く重要な一歩である。また、非平衡界面ゆらぎ現象は、KPZの名で知られる普遍的スケーリング則を示し、統計力学、数理物理学、確率論、ランダム行列理論など、物理学と数学の諸分野が関わる他、関連する自然現象も、確率的粒子輸送現象、スピン鎖、開放量子凝縮系など多岐に渡るため、そこにも大きな学術的意義がある。

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Published: 2025-01-30  

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