Spectral Analysis on the Schroedinger Operators with Matrix Coefficients and Its Applications

带矩阵系数的薛定谔算子的谱分析及其应用

• 批准号: 23540204
• 负责人: HIROKAWA Masao
• 金额: $ 3.24万
• 依托单位: Okayama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540204/
• 关键词: 行列係数を持つシュレディンガー作用素; ラビ模型; 超対称性; 自発的超対称性の破れ; ディラック作用素; 自己共役拡張; 境界条件; 量子ビット; シュレディンガー作用素; エネルギー準位交差; ２準位原子; １モード・レーザー光; 超対称量子力学; カイラル性; ラビ・ハミルトニアン; ジェインズ・カミングス・ハミルトニアン; 回路量子電磁力学; 結合定数; 強結合領域; 超強結合領域; 量子相転移

I had studied the Schroedinger operators with matrix coefficients in the light of the problems for controlling and transporting qubit. As for the former problem, I had made spectral analysis for the Rabi model and the Janes-Cummings model describing a 2-level (artificial) atom coupled with a 1-mode photon. I had investigated the mathematical properties on the energy as the coupling strength between the atom and the photon get larger. As for the latter problem, I had performed the research into the characterization of the quantum tunneling phase factor and the clarification of its mathematical properties.

我曾针对量子比特的控制和传输问题研究过具有矩阵系数的薛定谔算子。对于前一个问题，我对描述二能级原子与单模光子耦合的Rabi模型和Janes-Cummings模型做了谱分析。我研究了原子与光子之间的耦合强度增大时能量的数学性质。对于后一个问题，我进行了量子隧穿相位因子的表征和数学性质的澄清研究。

项目成果

Tunnel-Junction Formulae with Application to Spintronic Qubit

隧道结公式及其在自旋电子量子位中的应用

• 发表时间: 2013
• 作者: Fujii;Jun Ichi;橋本隆司;M. Hirokawa and T. Kosaka;肥田野 久二男;I. Sasaki;M. Hirokawa
• 通讯作者: M. Hirokawa

One-Dimensional Tunnel-Junction Formula for Schringer Particle

施林格粒子的一维隧道结公式

• DOI: 10.1088/1742-6596/302/1/012044
• 发表时间: 2013
• 期刊: SIAM Journal on Applied Mathematics
• 影响因子: 1.9
• 作者: Fujii;Jun Ichi;橋本隆司;M. Hirokawa and T. Kosaka
• 通讯作者: M. Hirokawa and T. Kosaka