Studies of condensed matter physics in terms of operator inequalities

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400123
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hokkaido University
• Principal Investigator: Miyao Tadahiro 北海道大学, 理学(系)研究科(研究院), 准教授 (20554421)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: フレーリッヒ模型 / 作用素不等式 / ハバード模型 / 長距離電荷秩序 / スピン鏡映正値性 / 量子電磁場 / 電子格子相互作用 / 汎関数積分

Outline of Final Research Achievements

(1) I studied some operator inequalities associated with self-dual cones. By applying these operator inequalities, I constructed a novel method of analyzing removal of the ultraviolet cutoff for the Froehlich model. By the method, I solved a longstanding problem, that is, I proved uniqueness of ground states for the Froehlich model. These results are published in international journals.
(2) I investigated a many-electron system coupled to the quantized radiation field. I obtained a useful upper bound of the charge susceptibility of the system. As a result, I proved the absence of long-range charge order. This result is published in an international journal.

Free Research Field

数理物理学