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

针对量子比特的控制和传输问题，研究了矩阵系数的薛定谔算子。对于前一个问题，我已经对Rabi模型和描述2能级（人工）原子与1模光子耦合的Janes-Cummings模型进行了光谱分析。我研究了当原子和光子之间的耦合强度变大时能量的数学性质。对于后一个问题，我对量子隧穿相位因子的表征及其数学性质的澄清进行了研究。

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.