Strongly Correlated Quantum Systems

他们在这个项目中提议开展强关联量子系统的理论研究。这些系统的性质由于成分之间的相互作用(在它们的情况下是自旋或电子)而发生了巨大的变化。关联在系统中的重要性可以通过几种方式来增强：通过施加强磁场、通过降低系统的维度或通过增加这些组成部分之间的相互作用的强度。在这里，他们建议利用分数量子霍尔效应(FQHE)理论的发展所获得的知识来研究强磁场中的三维电子气体。同样的知识在应用一类变分波函数来研究一维电子气的性质时也是有优势的。他们还建议继续研究强磁场中的二维电子气。此外，最近发现的氧化铜层状超导体被认为是强关联系统，因为同一铜位上的电子之间存在极强的库仑相互作用。这些相互作用可能是它们的高温超导电性的原因，他们提出了一些研究，旨在了解它们的性质与相互作用强度的关系。

They propose in this project to carry out theoretical studies of strongly correlated quantum systems. The properties of such systems are drastically altered as a result of interactions among the constituents (spins or electrons in their case). The importance of correlations in a system can be enhanced in several ways: by the application of a strong magnetic field, by reducing the dimensionality of the system or by increasing the strength of interactions between these constituents. They propose here to study the three-dimensional-electron-gas in a strong magnetic field, using knowledge gained through the development of the theory of the fractional quantum Hall effect (FQHE). The same knowledge can be used with advantage in applying a class of variational wave functions to study the properties of the one- dimensional electron gas. They propose also to continue their studies of the two-dimensional electron gas in a strong magnetic field. Additionally, the recently discovered copper oxide layered superconductors are believed to be strongly correlated systems because of the extremely strong Coulomb interactions between electrons on the same copper site. These interactions may be responsible for their high-temperature superconductivity and they propose studies aimed at understanding the dependence of their properties on the interaction strength.