algebraic properties of spectral curves of Rabi model and non-commutative harmonic oscillators

2016 Fiscal Year Final Research Report

• Project/Area Number: 15K13445
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: HIROSHIMA FUMIO 九州大学, 数理学研究院, 教授 (00330358)
• Project Period (FY): 2015-04-01 – 2017-03-31
• Keywords: 非可換調和振動子 / スペクトル曲線 / ゼータ関数 / Rabi模型

Outline of Final Research Achievements

In this research we planned to investigate (1) crossing of the spectral curves of the quantum Rabi model and non-commutative harmonic oscillators, (2) the meromorphic continuation of the spectral zeta function of the Rabi model to the whole complex plane, and (3) zeros of Hurwitz spectral zeta function for arithmetic point of view.
We could progress the crossing of the spectral curves of the Rabi model and we are preparing a paper for submitting to some journal. We also made the asymptotic behavior of the spectral zeta function clear.
We gave talks concerning this research twice oversea conferences and three times in domestic ones.

Free Research Field

作用素論、確率解析、場の量子論