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An exact real time quantum dynamics preaveraged over imaginary time pathintegral is formulated for general condensed phase equilibrium ensemble. Thisformulation results in the well-known centroid dynamics approach upon filteringof centroid constraint, and provides a rigorous framework to understand andanalyze a related quantum dynamics approximation method called ring polymermolecular dynamics. The formulation also serves as the basis for developing newkinds of quantum dynamics that utilize the cyclic nature of the imaginary timepath integral.

Real time quantum dynamics preaveraged over imaginary time path  integral: A formal basis for both Centroid Molecular Dynamics and Ring  Polymer Molecular Dynamics