Gulliksen, Jake Steven2011-04-212011-04-212010http://hdl.handle.net/10179/2299A variationally optimised basis allows an accurate description of the quantum behaviour of ultra-cold atoms, even in the strongly correlated regime. A rescaling scheme corrects discrepancies caused by using a reduced Hilbert space. This approach also allows the modelling of experimentally realizable double-well potentials, which still reveals the maximally-entangled states seen in fixed basis models. Time dynamics of these double-well systems show macroscopic tunnelling between wells for bosons with a sufficient interaction strength. The many-body problem of interacting bosons in the highly-correlated regime is difficult. The number of basis states needed to describe this quantum system accurately quickly grows beyond computational reach. Rescaling the interaction strength proves a simple and effective method of calculating exact eigenvalues in a reduced Hilbert space. Bosonic systems in the double-well potential are investigated next. First, how different eigen-states depend on the interaction strength is examined. The variationally optimised method has advantages over a standard fixed basis method with the ability to model experimentally viable systems and explore more stronglycorrelated regimes. Secondly, tunnelling dynamics in the double well are studied, specifically for a system where all particles initially occupy a single well. Oscillations corresponding to collective tunnelling between wells are found in regimes where there are zero interactions or bosons lie in a maximally-entangled state. What governs the dynamics outside these two regimes is also considered.enThe AuthorBosonsOne-dimensional single-well potentialsOne-dimensional double-well potentialsMathematical physicsThesisQ112883403https://www.wikidata.org/wiki/Q112883403