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.
