2019 Fiscal Year Final Research Report
Research on the binding condition and the renormalization for a quantum system of Bose field coupled to a particle
Project/Area Number |
16K17612
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
|
Research Institution | Shinshu University |
Principal Investigator |
Sasaki Itaru 信州大学, 学術研究院理学系, 准教授 (50558161)
|
Project Period (FY) |
2016-04-01 – 2020-03-31
|
Keywords | 数理物理 / スペクトル解析 / Rabiモデル / Bogoliubov変換 / 時間作用素 / 自己共役作用素 |
Outline of Final Research Achievements |
(1) We proved a theorem that identifies the essential spectrum of discrete Laplacian by adding graph perturbation to a periodic graph. (2) We consider a generalized Rabi model, and we proved that the dressed photon appears in the ground state in a deep-strong coupling regime. (3) It is constructed that Schrodinger operators with slowly decaying potential that has a positive energy embedded eigenvalue. (4) Time operators for quantum walks are considered, and various examples are constructed. It is clarified that the relationship between the winding numbers and self-adjoint expansions of a time operator. (5) Algebraic Bogoliubov transformations that diagonalize the Hamiltonian of a pair theory are developed.
|
Free Research Field |
数理物理学
|
Academic Significance and Societal Importance of the Research Achievements |
上の成果の(1)は物性物理学に関連する結果であり,周期構造を持つグラフの本質的スペクトルが特定されることにより,本質的スペクトルの外にある固有値の数値計算が保証されるようになる。(2)は量子デバイスに関連する数学的結果である。(3)(4)(5)は量子物理系の数学的構造に関する研究である。
|