We present an iterative Monte Carlo path integral methodology for evaluating thermally averaged real-time correlation functions. Standard path integral Monte Carlo methods are used to sample paths along the imaginary time contour. Propagation of the density matrix is performed iteratively on a grid composed of the end points of the sampled paths. Minimally oscillatory propagators are constructed using energy filtering techniques. A single propagation yields the values of the correlation function at all intermediate time points. Model calculations suggest that the method yields accurate results over several oscillation periods and the statistical error grows slowly with increasing propagation time.
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