Theory of Superconductivity in Correlated Electron Systems

提出了一项广泛的超导理论研究计划，从高tc超导体超导机理的微观描述到高场铌钛超导磁体的磁通钉钉研究。在微观工作中，方法是为二维哈伯德模型的基态和激发态构造变分波函数。这位研究者最近在早期对基态的研究基础上，发现了激发态的一种表达方式。这些物质的能量和其他性质可以用研究者和其他人先前开发的数值技术来评估。他们还建议继续将这个模型的解析理论发展到有限温度，使用最近发现的熵映射到一个很好理解的统计力学问题。进一步的工作旨在利用实验中子散射数据作为输入来确定UPt3的微观相位。与威斯康星实验组的合作也将继续。用数值方法探索颗粒超导模型来解释弱连接超导体的性质。将得到不同磁通钉钉形貌（实验确定）下的Ginsburg-Landau方程的数值解。这两个项目将有助于优化氧化物和铌钛磁体的性能。

A program of braodly-based theoretical research into superconductivity is proposed, ranging from the microscopic description of the superconductive mechanism in high-Tc superconductors to the investigation of flux-pinning in high- field Niobium-Titanium superconducting magnets. In the microscopic work, the approach is to construct variational wavefunctions for the ground and excited states of the two- dimensional Hubbard model. The investigator has recently found an expression for the excited states, building on earlier work for the ground state. The energy and other properties of these can be evaluated using a numerical technic previously developed by the investigator and others. They also propose to continue to develop the analytic theory of this model to finite temperatures, using a recently discovered mapping of the entropy into a well- understood statistical mechanical problem. Further work aimed at determining the microscopic phase of UPt3 using experimental neutron-scattering data as input will be pursued. Collaboration with experimental groups at Wisconsin will also continue. The model of granular superconductivity to explain properties of weakly-connected superconductors will be explored by numerical methods. Numerical solutions of the Ginsburg-Landau equations for different flux-pinning morphologies (experimentally determined) will be obtained.. These last two projects will help to optimize the properties of oxide and Niobium-Titanium magnets.