In recent years, the application of statistical mechanics to nonequilibrium systems, and quite specifically the probabilistic modelling of nonequilibrium microscopic dynamics, has become a major research topic. However, in contrast to the equilibrium case, there is currently no general framework within which nonequilibrium systems are understood. Hence the aim of this thesis is to improve our understanding of nonequilibrium systems through the study of a range of systems with probabilistic microscopic dynamics and the collective phenomena - notably phase transitions and the onset of scaling regimes - that arise. In this thesis I briefly review general aspects of mathematical models of probabilistic dynamics (stochastic processes), with a particular emphasis on steady-state properties and the origin of phase transitions. Then I consider separately four specific types of nonequilibrium dynamics. Firstly, I introduce and solve exactly a model of a particle reaction system. The solution which employs commutation properties of the <i>q</i>-deformed harmonic oscillator algebra, reveals that phase transitions in the analytic form of the particle density as a function of time arise as a direct consequence of randomness in the reaction dynamics. I also use similar mathematical techniques to solve the partially asymmetric exclusion process, an important prototype of a physical system that is driven by its environment. This model is also found to exhibit phase transitions, although in this case their origins lies in the nonequilibrium interactions between the system and its surroundings. Then I examine the scaling behaviour associated with the nonequilibrium directed percolation continuous phase transition. This transition is related to the presence of an absorbing state and I provide evidence for such a transition in a wetting model that does not possess an absorbing state. Finally, I generalise the wetting model to two dimensions and study its interfacial scaling behaviour. This is found to belong to the Kardar-Parisi-Zhang universality class, although there are strong crossover effects - which I quantify - that obscure the scaling regime.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:641741 |
| Date | January 2001 |
| Creators | Blythe, Richard Alexander |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/10834 |
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