Quantum many body calculations: An improved weighted density approximation to electronic density functional theory and Monte Carlo studies of superfluid vortices

This thesis uses computational methods to investigate two very different many body problems. The first half develops a weighted spin-density approximation (WSDA) to the electronic exchange-correlation functional. The second half describes Monte Carlo simulations of the vortex excitation in superfluid helium.; After reviewing in Chapter 1 the current status of electronic density functional theory, Chapter 2 develops a fully non-local approximation to the exchange-correlation functional for electrons. The energy functional treats correlation locally and exchange in the WSDA. Atomic ground state energies within this approximation are much improved over those within the popular local spin-density approximation (LSDA). This formulation of the weighted spin-density functional is particularly efficient when applied to problems in quantum chemistry and therefore allows for the first tests of this type of functional on molecules. Results for bond lengths, dissociation energies, and vibrational frequencies for some first row dimers are somewhat disappointing. Chapter 3 argues that this deficit results from an unphysical inter-shell interaction, which underestimates the screening between valence electrons and therefore weakens the bonding. When this interaction is removed in a qualitative fashion, the molecular results show good agreement with experiment. While the resulting form is not elegant, it accurately describes molecular properties.; The second part of the thesis describes variational calculations of the properties of a quantum vortex line in both two and three dimensional helium. These Monte Carlo calculations are based on two variations of a "shadow" wave-function. The first generates a singular vortex by simply multiplying the ground state wave-function by a phase. The second form distributes the vorticity over a finite core by exploiting the properties of the "shadow" wave-function. We calculated the radial dependence of the density, velocity field and excitation energy and find that the latter hardly changes as the density is increased from equilibrium to near freezing. This result appears to provide an explanation of why the classical core parameter, obtained from fitting experimental data for the energy and velocity of large vortex rings, expands as the density increases. The last chapter then applies these results to study the binding of a {dollar}sp3{dollar}He impurity to a vortex.