A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems
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We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.
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Smith, Kyle K.G., Poulsen, Jens Aage, Nyman, Gunnar, et al.. "A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems." The Journal of Chemical Physics, 142, no. 24 (2015) AIP Publishing LLC.: http://dx.doi.org/10.1063/1.4922887.