以双分量Hubbard模型为出发在单粒子占据的约束下或者是从 Gor’kov传播子模型出发在与系统晶格点群对称群以及对势对称性相容的前提下，试图建立描述高温超导体对关联函数随掺杂度变化的物理模型；并由此推导量子态时间演化方程和自洽迭代条件. 通过理论分析与数值模拟，正确描述在物理参量空间涡旋量子态演化过程。研究量子受限尺寸效应和多序相互作用对涡旋态的对称性的影响、边缘态-体态对应规则；将重点关注空穴掺杂铜氧化物超导体磁通涡旋态对称性与拓扑序，描述其基本属性。将回答外部电磁场作用下赝能隙区量子态相位相干与否的问题。探索Hubbard模型框架下双粒子占据的可能性、建议并论证对其量子态相位相干调控方案. 为理解与拓展Anderson 绝缘态概念相关的基本物理问题、揭示铜氧化物超导体中绝缘-金属相变及其超导电性起因提供重要启示。

Based on a two-component Hubbard model under the single-particle occupied constraint or starting from the Gor'kov propagators equations with the crystal point group and pairing potential symmetry in mind, we will aspire to develop a model describing the pairing correlations as a function of the hole-doping level in cuprate high-temperature superconductors, from which the evolution equations for system quantum states and the self-consistent conditions are derived. Theoretical analyses and numerical simulations will be accomplished to correctly describe the vortex bound states evolution and quantum transitions in physical parameters space. The effects of the quantum confined and the competitions between different orderings on vortex core state symmetry, the edge-bulk correspondence rules will be specified, with emphasis on the symmetry and topological order of vortex core state of the hole-doped cuprate superconductors, and its basic nature. We will show whether the electromagnetic field induced phase-coherent state could be a ground state above the critical temperature or in the so-called pseudogap phase, to explore the possibilities of two-particle occupied state within the framework of the Hubbard model with large on-site repulsion, and to suggest and possible phase-coherent control approaches. We expect such in-depth and systematic investigations will provide important informations and clues in promoting ones understanding on the fundamentals physics like the conjecture of extend Anderson insulating state, and in revealing the insulator-metal transition and the high-Tc superconductivity origins in cuprate superconductors.