Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Part I. We analyze a gravity wave detector consisting of a Weber type resonant antenna, an inductive transducer and a dc SQUID coupling system. We derive the complete set of equations of motion for the system and discuss their implications and solutions in detail. The results obtained are applied to the LSU gravity wave detector, and the optimum system parameters are calculated. We show that it is possible to approach quantum limited sensitivity for the detector if these optimum system parameters and matching conditions are properly satisfied. In the final chapter we present our preliminary experimental results. We have built an electronic feedback system and operated a very sensitive and well coupled planar dc SQUID at liquid helium temperature. The parameters and characteristics of dc SQUID, the dynamic property of feedback loop, and the noise performance of the system have been carefully measured. Part II. We first present a critical comparison of the work of Ramana and Rajagopal (RR) with the work of McDonald (MD) on the spin polarized relativistic electron gas system. After correcting some errors in previous work of RR, a new analytical expression for exchange energy and exchange potential which are convenient for practical applications are then derived. We have therefore set up the correct relativistic generalization of spin density functional theory. We prove that, in general, the mapping V((')r,t) (--->) (')J((')r,t), is not invertible for a given initital condition, and a particle density func- tional theory comparable to the HK Theorem for stationary problems cannot be established for general time-dependent systems. We suggest a new current density functional theory for time-dependent systems. We emphasize that (')J((')r,t) instead of n((')r,t) plays a central role in time-dependent problems. In chapter IV, we examine the effects of the underlying crystal structure and the surface/interface normal on spin waves at surfaces and interfaces for cubic crystals described by the Heisenberg Hamiltonian. Our detailed numerical results show that, with the same perturbations, there are pronounced differences in the results obtained for different faces of the same crystal, or in those for the same face of different crystals.