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    Applications of Lie symmetry analysis to the quantum Brownian motion model.

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    NaickerV_2009thesis.pdf (296.5Kb)
    Date
    2008
    Author
    Naicker, Viroshan.
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    Abstract
    Lie symmetry group methods provide a useful tool for the analysis of differential equations in a variety of areas in physics and applied mathematics. The nature of symmetry is that it provides information on properties which remain invariant under transformation. In differential equations this invariance provides a route toward complete integrations, reductions, linearisations and analytical solutions which can evade standard techniques of analysis. In this thesis we study two problems in quantum mechanics from a symmetry perspective: We consider for pedagogical purposes the linear time dependent Schrodinger equation in a potential and provide a symmetry analysis of the resulting equations. Thereafter, as an original contribution, we study the group theoretic properties of the density matrix equation for the quantum Brownian motion of a free particle interacting with a bath of harmonic oscillators. We provide a number of canonical reductions of the system to equations of reduced dimensionality as well as several complete integrations.
    URI
    http://hdl.handle.net/10413/455
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    • Masters Degrees (Physics) [134]

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