Theoretical analyses of first-order phase transitions using generalized ensembles

2021 Fiscal Year Final Research Report

• Project/Area Number: 19H01810
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: The University of Tokyo
• Principal Investigator: Shimizu Akira 東京大学, 大学院総合文化研究科, 教授 (10242033)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: 相転移 / 相共存 / 統計力学 / 統計集団

Outline of Final Research Achievements

The first-order phase transition is a widely-observed phenomena that are important in many fields of science and technology including physics, chemistry, biology and engineering. Despite such importance, theoretical studies were not made sufficiently because the conventional statistical ensembles have many problems. For example, at a phase transition point some of them become ill-defined whereas others become unstable. We have resolved these problems in this work by (i) proposing a novel class of statistical ensembles, (ii) deriving useful formulas specific to these ensembles, and (iii) developing concrete methods of calculations.

Free Research Field

物性基礎論

Academic Significance and Societal Importance of the Research Achievements

一次相転移と、それに伴う相共存現象は、物理学にとどまらず、化学、生物学、工学の広い分野にわたって極めて重要になっている。その重要な現象について、従来の物理学は十分に答えることができなかったのに対して、本研究によって、根本的な問題が解決することができた。今後は、この成果を様々な具体例に応用することによって、上記のような広い科学・技術分野において、新しい知見が得られる可能性を開拓することができた。