Rigorous construction of many-electron systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 26870110
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics; Foundations of mathematics/Applied mathematics
• Research Institution: Osaka University (2017); The University of Tokyo (2014-2016)
• Principal Investigator: Kashima Yohei 大阪大学, 数理・データ科学教育研究センター, 特任助教(常勤) (20648282)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 多体電子系 / 数理物理学 / 数理解析学 / 量子統計力学 / 繰り込み群

Outline of Final Research Achievements

In this research project I analyzed quantum many-body systems of electrons hopping and interacting on a crystalline lattice at positive temperature. Physical quantities of the systems are defined within the framework of quantum statistical mechanics. It is an important theme of today's mathematical physics to rigorously analyze many-electron systems in low temperatures by keeping the intensity of electrons' interaction positive. Renormalization group method is believed to be effective to improve the temperature-dependency of allowed magnitude of interaction. The main achievement of this research project is that mathematical analysis of interacting many-electron systems in wide temperatures regions down to zero-temperature was made possible by rigorous construction of renormalization group methods.

Free Research Field

数理物理学、応用解析学