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

点击翻译按钮获取中文摘要

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.