| Summary: | Almost all quantum systems are open; interactions with the surrounding environment generally lead to complex dissipative behaviour with a sensitive dependence on the details of the system-environment coupling. This thesis presents results from theoretical investigations into such behaviour in single and two-site quantum systems with a particular emphasis on strong system-environment coupling regimes, and also the effects of spatial correlations in the environment fluctuations. Within a weak system-environment coupling framework, it is found that an increased level of correlation is able to protect coherence shared between two spatially separated two-level quantum systems. Moreover, it is found that these correlations are in fact able to generate coherence between the two systems, and in certain regimes, cause the systems to become entangled. Using a polaron transform strong coupling master equation technique, the discussion is extended to the strong system-environment coupling or high temperature regime. To assess the validity of this approach in an experimentally relevant system, it is applied to the description of excitonic Rabi oscillations in a resonantly driven quantum dot. For most of the parameters of interest, the strong coupling theory is found to be valid over a far greater range of temperatures and coupling strengths than the standard weak-coupling theory. The coherent or incoherent nature of energy transfer dynamics is then studied by applying the strong coupling theory to a donor-acceptor pair model. Increased spatial correlations are found to extend the range of temperatures which allow coherent energy transfer to take place. Finally, a variational theory is introduced which allows for exploration of certain parameter regimes where both the weak-coupling and strong coupling theories become invalid. The variational theory is then used to investigate the ground state properties of a double two-level impurity model. High levels of spatial correlation are found to suppress the tunnelling amplitude within each impurity.
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