Universität Rostock, 2016
Abstract: Understanding the dynamics of complex molecular systems is one of the most important and challenging issues in physics. The theoretical investigation of the (non-)linear spectra can provide an insight to the underlying mechanisms. This thesis is dedicated to the path integral (PI) formulation of quantum mechanics and its applicability to infra-red spectroscopy. The promising features of that formalism lie in the absence of any approximations. Starting from a system-bath partitioning all necessary expressions are rigorously derived to propagate time-dependent expectation values and equilibrium time-correlation functions within the PI framework. The resulting equations of motion are discretized and translated into a source code that is kept generally and requires as input only the numerical parameters as well as system and bath characteristics. The self-implemented methodology is tested against published literature. Furthermore, the applicability of the discrete PI formalism to simulate the quantum dynamics of electron transfer and vibrational systems coupled to realistic solvents is investigated. It turns out that the methodology is not apropriate for the latter, while it is perfectly suitable for the former. The reason is traced back unambiguously to intrinsic features of the vibrational system itself and cannot be circumvented employing nowadays computational means.
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