New Analytic and Computational Techniques for Finite Temperature Condensed Matter Systems

By employing a special summation technique we find that the breakdown of the Meissner-Ochsenfeld effect in the three dimensional Bose gas as the applied field passes through its critical value is an entropy driven weakly first order transition, rather than the second order transition usually ascribed to the system. The transition is second order at the usual Bose condensation temperature T_{c} as well as at T = 0, with a line of first order transitions connecting these critical points. The first order transitions make the Bose gas resemble familiar superconductors, and a Landau -Ginzburg analysis indicates that the Bose gas is always a type I superconductor. We employ the recently introduced conjugate-gradient methods for minimization of the electronic energy functional to perform an extensive ab initio study of the Sigma = 5 tilt (310) grain boundary in germanium. We find that the boundary reliably reconstructs to the tetrahedrally bonded network observed in HREM experiments without the proliferation of false local minima observed in similar twist boundaries. The reduced density of bonds crossing the grain boundary plane leads us to conjecture that the boundary may be a preferred fracture interface. We then combine these conjugate-gradient methods with a new technique for generating trial wavefunctions to produce an efficient ab initio molecular dynamics scheme that is that is at least two orders of magnitude more accurate than previous schemes and thus allows accurate calculation of dynamic correlation functions while maintaining tolerable energy conservation for microcanonical averages of those correlation functions over picosecond time scales. We present two advances which greatly enhance the efficiency of our new ab initio molecular dynamics technique. We introduce a class of generalizations of traditional Fermionic energy functionals which allow us to lift the orthonormality constraints on the single particle orbitals and thus speed convergence by permitting more general paths toward the minimum. We present important insights into the general computational physics problem of the iterative solution for the state of a complex system as a function of some continuously varying external parameter. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.) (Abstract shortened with permission of school.).