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Advances in Path Integral Methodology A promising approach to the quantum dynamics of condensed-phase systems is Feynman’s path integral formulation of time-dependent quantum mechanics. This formulation avoids the unrealistic memory demands of the Schrödinger equation at the cost of introducing auxiliary integration variables (often referred to as "beads"). Monte Carlo techniques are ideally suited for evaluating the path integral in imaginary time, leading to the powerful Path Integral Monte Carlo method for simulating the equilibrium properties of many-body quantum systems. However, the real-time path integral involves a rapidly oscillatory phase (the essence of quantum interference), which renders the convergence of Monte Carlo integration methods exponentially slow. Our group pioneered the development of an iterative path integral methodology for systems interacting with dissipative harmonic media, which exploits the decoherence induced by a condensed phase environment on the dynamics of the system of interest. This approach has also been generalized, leading to the formulation of an iterative path integral methodology for systems in general anharmonic environments. The latter stems from a deeper understanding of the structure of influence functionals, which also leads to a path integral perspective on the linear response approximation and its lowest order corrections.
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