A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems

Kyle K G Smith; Jens Aage Poulsen; Gunnar Nyman; Peter J Rossky

doi:10.1063/1.4922887

A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems

J Chem Phys. 2015 Jun 28;142(24):244112. doi: 10.1063/1.4922887.

Authors

Kyle K G Smith¹, Jens Aage Poulsen², Gunnar Nyman², Peter J Rossky³

Affiliations

¹ Institute for Computational Engineering and Sciences and Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA.
² Physical Chemistry, Department of Chemistry and Molecular Biology, University of Gothenburg, SE 41296 Gothenburg, Sweden.
³ Department of Chemistry, Rice University, Houston, Texas 77251, USA.

PMID: 26133415
DOI: 10.1063/1.4922887

Abstract

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.