This dissertation deals with theory and algorithms for computer simulations
of classical and quantum systems in the canonical ensemble. First,
the approach of Nos e-Hoover and its generalization, known as the Nos e-
Hoover chain dynamics, are introduced. Such methods are used in classical
molecular dynamics simulations to control the temperature of particle systems
through a coupling to a few additional fictitious variables, mimicking
an in nite thermal reservoir. In order to introduce the extension of the
Nos e-Hoover method to quantum systems, the features of the Wigner representation
of quantum mechanics are reviewed. Finally, a recent approach
[A. Sergi and F. Petruccione, J. Phys. A 41 355304 (2008)], which extends
the Nos e-Hoover and Nos e-Hoover chain equations in quantum phase space,
is described. Such a method is applied to a single harmonic mode, and the
conditions for quantum-to-classical transitions as a function of the thermodynamical
temperature are studied by means of numerical simulations. It
is shown that, in the case of strong coupling, the open system dynamics
simulated by Nos e-Hoover chain equations leads to quantum-classical transition
of the Wigner function of the harmonic mode. Agreement between
the numerical and analytical results is also found. The algorithms and results
illustrated are of interest to the numerical simulation of the quantum
dissipative dynamics of more general systems. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/7776 |
| Date | January 2011 |
| Creators | Megnidio-Tchoukouegno, Mireille Merlise. |
| Contributors | Sergi, Alessandro. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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