Theory of Superconductivity in Correlated Electron Systems

一个基于头脑的理论研究计划， 超导电性提出，从微观 高温超导体的超导机制 超导体的磁通钉扎研究在高- 场铌-钛超导磁体。 在 微观工作，方法是构造变分的 这两种物质的基态和激发态的波函数 三维Hubbard模型 调查人员最近发现， 在早期工作的基础上， 对于基态。 这些物质的能量和其他性质 可以使用先前开发的数字技术进行评估 调查员和其他人。 他们还建议继续 将该模型的解析理论发展到有限温度， 利用最近发现的熵映射到一个阱中， 理解统计力学问题。 进一步的工作旨在 用实验方法确定UPt 3的微观相 中子散射数据作为输入将被追踪。 协作 在威斯康星州的实验小组也将继续。 的 颗粒超导性模型来解释 弱连接超导体将通过数值模拟来探索 方法. Ginsburg-Landau方程的数值解 对于不同的磁通钉扎形态（实验上 将获得（）。最后两个项目将有助于 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.