| Summary: | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2006. === Vita. === Includes bibliographical references. === In this thesis, we develop analytical models for quantum systems and perform theoretical investigations on several dynamical processes in condensed phases. First, we study charge-carrier mobilities in organic molecular crystals, and develop a microscopic theory that describes both the coherent band-like and incoherent hopping transport observed in organic crystals. We investigate the structures of polaron states using a variational scheme, and calculate both band-like and hopping mobilities at a broad range of parameters. Our mobility calculations in 1-D nearest-neighbor systems predict universal band-like to hopping transitions, in agreement with experiments. Second, motivated by recent developments in quantum computing with solid-state systems, we propose an effective Hamiltonian approach to describe quantum dissipation and decoherence. We then applied this method to study the effect of noise in a number of quantum algorithms and calculate noise threshold for fault-tolerant quantum error corrections (QEC). In addition, we perform a systematic investigation on several variables that can affect the efficiency of the fault-tolerant QEC scheme, aiming to generate a generic picture on how to search for optimal circuit design for real physical implementations. === (cont.) Third, we investigate the quantum coherence in the B800 ring of' of the purple bacterium Rps. acidophila and how it affects the dynamics of excitation energy transfer in a single LH2 complex. Our calculations suggest that the coherence in the B800 ring plays a significant role in both spectral and dynamical properties. Finally, we discussed the validity of Markovian master equations, and propose a concatenation scheme for applying Markovian master equations that absorbs the non-Markovian effects at short times in a natural manner. Applications of the concatenation scheme on the spin-boson problem show excellent agreements with the results obtained from the non-Markovian master equation at all parameter range studied. === by Yuan-Chung Cheng. === Ph.D.
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