Complex quantum phenomena can often be understood more easily by identifying a relevant system and an environment which interacts with the system. Numerically exact methods for these dissipative quantum systems are discussed with particular focus on their dynamics. Using the dissipative two-state system and charge transport through a mesoscopic metallic island as illustrative examples, we present algorithms based on the importance sampling of Feynman path integrals as well as novel techniques relying on the numerical simulation of stochastic Liouville-von Neumann equations.
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