a Theory of Many-Component Interacting Fermi Systems.

Ph. Nozières, Daniel W. Hone, M. E. Rose

Tai Kai Ng, K. S. Singwi

A systematic way of deriving effective interactions for self-energy calculations in Fermi-liquid systems is presented. The self-energy expression contains effects of density and spin fluctuations and also multiple scattering between particles. Results for arbitrarily polarized one-component Fermi-liquid systems and unpolarized two-component systems are explicitly given.

Philippe Nozières

Benjamin M. Fregoso

This thesis is devoted to the study of quantum liquid crystal phases in metallic systems and itinerant Fermi systems with dipole-dipole interactions. It is based on published works of Refs. [65, 193, 68, 67, 66]. In the first part of the Thesis, I present the construction of a generalization of the the McMillan- de Gennes theory of nematic-smectic thermal phase transition of classical liquid crystals to describe an analogous quantum phase transition in metallic systems. This theory qualitatively can also describe similar quantum phase transitions in high Tc superconductors. Recent experimental advances in cooling atoms with large electric or magnetic moment[125] make possible the study of novel quantum phases that arise due to the anisotropic and long-range nature of the dipole-dipole interactions. In the next part of the Thesis I present a Landau Fermi liquid theory of one-component Fermi systems with electric or magnetic dipolar interactions. I use this theory to construct an order parameter theory and predict elongated Fermi surface(FS) along the polarization axis. I calculate the temperature and interaction dependence of FS distortions. For a two-component system with magnetic dipole-dipole interactions I predict the existence of “spin textures” in momentum space and of prolate/oblate deformed FS’s. This constitutes a new phase of matter I called ferronematic. Possible observation of this phase in ultracold Fermi gases with large mangnetic moments

Yajiang Hao, Shu Chen

We investigate the ground-state properties of two-component Bose gases confined in one-dimensional harmonic traps in the scheme of density-functional theory. The density-functional calculations employ a Bethe-ansatz-based local-density approximation for the correlation energy, which accounts for the correlation effect properly from the weakly interacting regime to the strongly interacting regime. For the binary Bose mixture with spin-independent interaction, the homogeneous reference system is exactly solvable by the Bethe-ansatz method. Within the local-density approximation, we determine the density distribution of each component and study its evolution from Bose distributions to Fermi-like distribution with the increase in interaction. For the binary mixture of Tonks-Girardeau gases with a tunable interspecies repulsion, with a generalized Bose-Fermi transformation we show that the Bose mixture can be mapped into a two-component Fermi gas, which corresponds to exact soluble Yang-Gaudin model for the homogeneous system. Based on the ground-state energy function of the Yang-Gaudin model, the ground-state density distributions are calculated for various interspecies interactions. It is shown that with the increase in interspecies interaction, the system exhibits composite-fermionization crossover.

R. F. Bishop