The equilibrium statistical behavior of phase flows on surfaces of complicated topology is studied. Both classical tools developed in the theory of Riemann surfaces and numerical methods associated with discrete mathematics (graph theory) are applied to the characterization of the equilibrium statistical behavior of systems with U(1) symmetry on two-dimensional manifolds. The relation between a surface's topology and physical parameters such as the superfluid density, vortex core shape and boundary effects is investigated. The effect of quantization is traced through the characterization of states via the Hodge decomposition and in the partition function. It is shown that for surfaces of an appropriate shape a new type of Kosterlitz-Thouless transition is possible. This situation is novel because quantized vortices are required only for ergodicity and the disordering of the superfluid/normal phase transition is by fluctuations in the nonsingular harmonic flows.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-8355 |
| Date | 01 January 1992 |
| Creators | Reinhold, Bruce Bennett |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
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