Strongly interacting fermion systems

Abstract

Research has been concentrated primarily in three areas: heavy fermions, physics of high-temperature superconductivity, and electronic properties. In heavy fermions a peak in the attenuation coefficient of ultrasound just below the superconducting transition temperature can be explained in the context of conventional (BCS) superconductivity theory by recognizing how profoundly that theory is reorganized in heavy fermion systems in which the sound velocity. In high-temperature superconductors there have been development of a model for magnetism in one alloy which shows unusual first-order phase transitions in a magnetic field, a possible mechanism for high-temperature superconductivity based on an electric quadrupole moment of Cu in tetragonal crystal geometry, and a neat resolution of a paradox between a theory connecting gaps in spectrum with the degeneracy of the system and a prominent current theoretical view that there is a gap and no degeneracy. It turns out there is topological degeneracy that had been previously recognized. In electronic structure we have shown that the finite element approach can be used for electronic systems with an efficient code using more than a half-million local basis functions. In addition, we have developed a variational principle for determining optimal meshes for solving differential equations--such as the Schroedinger equation.