Scaling limits for one-dimensional large scale interacting systems

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K20332
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: Keio University
• Principal Investigator: Suda Hayate 慶應義塾大学, 理工学研究科(矢上), 研究員 (80912386)
• Project Period (FY): 2021-08-30 – 2024-03-31
• Keywords: 箱玉系 / Box-Ball System / 確率調和振動子鎖 / 大規模相互作用系 / スケール極限

Outline of Final Research Achievements

(1)We introduce a new linearization method for the box-ball system, called "seat number configuration". This also gives a relationship between several existing linearization methods for the box-ball system. By utilizing the seat number configuration, it is expected that the space-time scaling limits for box-ball systems in more general situations will become possible, and partial results have already obtained.
(2)We consider the behavior of macroscopic heat diffusion for stochastic harmonic chains, where a new tyoe of boundary condition is imposed at the origin. Although there was a delay in starting the research due to the pandemic and it was not completed during the term of the grant, it is progressing well.

Free Research Field

数物系科学

Academic Significance and Societal Importance of the Research Achievements

巨視的な物理現象を微視的な数理模型から厳密に導出することは, 統計力学に動機づけられた重要な問題である. 本研究課題では, 具体的な微視的系に関して, その巨視的振る舞いを導出するために必要な数学的道具の構成, またそれを用いた時空スケール極限の考察が行われた. これは, 統計力学的な問題に数学的基礎づけを与えるものである.
「普遍性」の観点からは, 類似した数学的構造を持つ微視的系に対しても同様の結果が得られることが期待されるため, 本研究成果は関連する研究分野に今後の研究指針を与えるものとしても意味のあるものである.