A Hartree-Fock approach is used to approximate the equilibrium and dynamic properties of an ultra-cold Bose gas in various potentials. The required set of single-particle wave functions and energies are derived using a technique that relies on the Bogoliubov inequality. Furthermore, both the ground and excited states are determined by a single Hamiltonian, hence enabling the use of variational principles to locate the natural frequencies. The example systems are all one-dimensional: a harmonic trap, and a ring-trap with and without a periodic potential superimposed. The natural frequencies are shown to have a weak dependence on temperature, whereas the influence of the interaction strength can be significant.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:659187 |
| Date | January 2014 |
| Creators | Bevan, Stephen |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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