The dynamics of non-interacting, ultracold alkali atoms in the presence of counter-propagating lasers (optical lattice systems) is considered theoretically. The center of mass motion of an atom is such a system can be described by an effective Hamiltonian of a relatively simple form. Modulation of the laser fields implies a parametric variation of the effective Hamiltonian's eigenvalue spectrum, under which avoided crossings may occur. We investigate two dynamical processes arising from these near-degeneracies, which can be manipulated to coherently control atomic motion. First, we demonstrate the mechanism for the chaos-assisted, or multiple-state, tunneling observed in recent optical lattice experiments. Second, we propose a new method for the coherent acceleration of lattice atoms using the techniques of stimulated Raman adiabatic passage (STIRAP). In each case we use perturbation analysis to show the existence of a small, few level, subsystem of the full effective Schrödinger equation that determines the dynamics. / text

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We produce a nonpositively curved square complex, X, containing exactly four squares. Its universal cover, X̃ ≅ T4 x T 4, is isomorphic to the product of two 4-valent trees. The group, pi1X, is a lattice in Aut (X̃) but π1X is not virtually a nontrivial product of free groups. There is no such example with fewer than four squares. The main ingredient in our analysis is that X̃ contains an "anti-torus" which is a certain aperiodically tiled plane.

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Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.

The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns itself mainly with correlations between results in classical hierarchies and quantum lattice models. The second part, consisting of chapters 4-6, deals almost entirely with deriving results concerned with quantum lattice models.

Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2002. / Bibliography: leaves 124-127.

Thesis (Ph.D.)--University of Adelaide, School of Chemistry and Physics, Discipline of Physics, 2004. / Bibliography: p. 222-229.

Thesis (Ph.D.). / Written for the Computational Acoustic Modeling Laboratory, School of Music. Title from title page of PDF (viewed 2008/01/12). Includes bibliographical references.