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In a thermally equilibrated system, electron behavior in a metal is described by the Fermi-Dirac equation. With ultrafast lasers, electrons can be excited into temporary distributions which are not described by the Fermi-Dirac equation and are therefore not at a well-defined temperature. These nonthermal distributions quickly equilibrate through two primary processes: electron-electron scattering and electron-phonon scattering. In most situations, these effects are unnoticeable, since they are completed within 5 ps. A probabilistic numerical model for electron-electron scattering is presented. The model is robust, scaleable, and requires only one parameter. The success of the model suggests future work on a similar electron-phonon scattering model, which would provide a complete description of the elctron distribution during thermalization. Once complete, this model can be tested by measuring the amount of second harmonic light generated by an ultrafast laser in a pump-probe experiment.

Thesis (Ph.D.)--York University, 2008. Graduate Programme in Physics and Astronomy. / Typescript. Includes bibliographical references (leaves 123-130). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR45983

Thesis (M. Sc.)--York University, 1999. Graduate Programme in Physics. / Typescript. Includes bibliographical references (leaves 115-116). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pMQ39187.

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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 49-50). Also available in electronic version. Access restricted to campus users.

Thesis (doctoral)--Bonn, 1998. / Includes bibliographical references (p. 84-86).

Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 1, 2007) Vita. Includes bibliographical references.

This thesis discusses the two dimensional allotrope of carbon known as graphene in presence of magnetic field, with special focus on edge states. The structure of graphene is described in detail and from the structure, two models are formed. The Dirac equation is a good description of graphene for large samples, far away from edges, where the boundaries can be ignored. However, it causes problems with most types of edge and hard wall approximation has to be implemented. The Dirac equation is described in detail and used to obtain an energy spectrum, wavefunction and density of states for graphene edge in a strong magnetic field. For comparison, a Bohr-Sommerfield approximation was used to find the dispersion relation and compare it to the results obtained numerically from the Dirac equation. The second model, better fitting for nano-scale systems, is the tight binding model. This model was utilized to find Energy spectrum for graphene flakes in magnetic field, which resembles Hofstadter's butterfly spectrum. The spectrum was analyzed and periodic oscillations of magnetisation dependent on magnetic field (known as the de Haas-van Alphen effect) were described. The oscillation of magnetisation depends on the shape of the dot, even though the main properties remain the same: at low magnetic field, periodic oscillations due to Aharonov-Bohm effect, turning into more chaotic oscillations depending on the boundary conditions of the given quantum dot.

The connection discovered by M. Sato, T. Miwa and M. Jimbo (SMJ) between the monodromy-preserving deformation theory of the two-dimensional Euclidean Dirac operator and quantum fields is rigorously established for the case of nonreal S¹ monodromy parameters. This connection involves the expression of the associated n-point functions in terms of solutions to deformation equations which arise as necessary conditions for the monodromy exhibited by a class of multivalued solutions of the Euclidean Dirac equation to be preserved under perturbations of branch points. Our approach utilizes recent results involving infinite-dimensional group representations. A lattice version of the n-point function is introduced as a section of a determinant bundle defined over an infinite dimensional Grassmannian. A trivialization for this bundle is singled out so that the corresponding n-point functions behave like Ising correlations in the massive scaling regime. Then the SMJ n-point functions are recovered as the scaled functions. A parallel scaling analysis is carried out with lattice analogues of the Euclidean Dirac wave functions which scale to square-integrable multivalued solutions of the Euclidean Dirac equation and the connection between the SMJ deformation theory and the n-point functions is rigorously established in terms of local Fourier expansion coefficients of these wave functions. These results are presented in detail for two-point functions with the same monodromy associated to each site.