Microscopic and hydrodynamics approaches to nonequilibrium statistical mechanical models

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K03665
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Sasamoto Tomohiro 東京工業大学, 理学院, 教授 (70332640)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: non-equilibrium / fluctuations / Kardar-Parisi-Zhang / exclusion process / hydrodynamics / large deviation

Outline of Final Research Achievements

In this research project, we were able to obtain highly novel results from both microscopic and hydrodynamic points of view. First, from a microscopic point of view, we found a relation between models belonging to the Kardar-Parisi-Zhang (KPZ) universal class and free fermions. This will be very useful and important in future studies of systems exhibiting KPZ fluctuations. From a hydrodynamics point of view, we have extended the framework of generalized hydrodynamics (GHD) to the one which can capture non-equilibrium fluctuations at the level of large deviations. This will be important in future investigations of fluctuations in systems with multiple conserved quantities. Furthermore, we have given the first analytic conformation of a prediction of non-linear fluctuating hydrodynamics for a microscopic model with stochastic dynamics.

Free Research Field

非平衡統計力学

Academic Significance and Societal Importance of the Research Achievements

平衡系と比較して、非平衡多体系における揺らぎの研究はまだまだ未発達の部分が大きい。KPZ揺らぎも、一般化流体力学で記述される系も、非線形揺らぐ流体力学も、非平衡多体系において普遍的に現れるものがであることが近年ますます明らかとなってきている状況であり、本研究課題における解析計算を用いた理論的研究成果は、非平衡多体系における揺らぎに関する基礎的な理解を大きく進めるものである。また、非平衡多体系の実験も近年増えてきていることから、本研究の理論的研究成果は今後実験においても検証され、基礎的な役割を果たすことが期待される。