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We investigate the usage of a recently introduced noise-cancellationalgorithm for Brownian simulations to enhance the precision of measuringtransport properties such as the mean-square displacement or thevelocity-autocorrelation function. The algorithm is based on explicitly storingthe pseudo-random numbers used to create the randomized displacements incomputer simulations and subtracting them from the simulated trajectories. Theresulting correlation function of the reduced motion is connected to the targetcorrelation function up to a cross-correlation term. Using analytical theoryand computer simulations, we demonstrate that the cross-correlation term can beneglected in all three systems studied in this aper. We further expand thealgorithm to Monte Carlo simulations and analyze the performance of thealgorithm and rationalize that it works particularly well for unbounded, weaklyinteracting systems in which the precision of the mean-square displacement canbe improved by orders of magnitude.

Noise-cancellation algorithm for simulations of Brownian particles