stochastic physics of disordered systems by persistent homology

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K13530
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: National Institute of Advanced Industrial Science and Technology (2017); Tohoku University (2015-2016)
• Principal Investigator: Nakamura Takenobu 国立研究開発法人産業技術総合研究所, 材料・化学領域, 主任研究員 (10642324)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 統計物理学 / パーシステントホモロジー / トポロジカルデータ解析 / 確率過程 / 自由エネルギー

Outline of Final Research Achievements

We have found that persistent homology is useful for describing amorphous structures. As a remarkable result, (1) it is possible to handle amorphous structures that take qualitatively different forms called silica glasses, metallic glasses in a unified way (2) a hidden structure embedded in the disordered structure can be extracted by the persistent homology. Furthermore, we have developed a framework to express the physical properties by using the method to represent disordered structure. Specifically, we have developed the the procedure to calculate free energy landscape for abstractly defined variables such as variables in persistent homology by using stochastic process.

Free Research Field

統計物理学