Operator and Spectral Analyses for Differential Operators with Matrix-Coefficient

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400117
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hiroshima University
• Principal Investigator: HIROKAWA Masao 広島大学, 工学研究科, 教授 (70282788)
• Co-Investigator(Renkei-kenkyūsha): KAWABI Hiroshi 岡山大学, 大学院自然科学研究科, 教授 (80432904)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 回路電磁気学 / 一般化された量子ラビ模型 / ディラック粒子 / 接合を持った量子細線 / 深強結合領域

Outline of Final Research Achievements

In this research program, we considered the following two mathematical models. (1) We studied some quantum effects mainly for the generalized quantum Rabi model among non-commutative harmonic oscillator models. In particular, in the light of circuit QED, we made operator and spectral analyses for that model, and we mathematically clarified its bound state in the deep-strong coupling regime. Meanwhile, (2) for the model of the two quantum wires with a junction between the two, we clarified how the electron's wave function have a phase factor, and how the electron spin has an effect when the electron as a Dirac particle passes through the junction.

Free Research Field

数理物理学