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Our desire to optimize the design of quantum technologies and our thirst for understanding quantum effects in biological phenomena have lead to an explosion of interest in predicting density operator dynamics of large open quantum systems. Exact methods are currently in very high demand for benchmarking the recent surge of new methods developed for such systems. Two of these methods are the Quasiadiabatic propagator Path Integral (QUAPI) and the Hierarchical Equations of Motion (HEOM) - both which have serious limitations on the size of the aggregates being considered. I will present a method that significantly increases the system size tractable for QUAPI, and a method that increases the accuracy of HEOM. I will then apply these methods to excitation dynamics in driven GaAs quantum dots and energy transfer in the FMO light-harvesting complex. |