Real time correlation function in a single phase spaceintegral--beyond the linearized semiclassical initial valuerepresentation

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It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are ... continued below

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Liu, Jian & Miller, William H. July 10, 2007.

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It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the 2nd order WD based on 'Winger trajectories', and the full Donoso-Martens dynamics (full DMD) and the 2nd order DMD based on 'Donoso-Martens trajectories'--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of these four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (non-linear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.

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  • Journal Name: Journal of Chemical Physics; Journal Volume: 126; Related Information: Journal Publication Date: June 19,2007

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  • Report No.: LBNL--63117
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.1063/1.2743023 | External Link
  • Office of Scientific & Technical Information Report Number: 928591
  • Archival Resource Key: ark:/67531/metadc900263

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  • July 10, 2007

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  • Sept. 27, 2016, 1:39 a.m.

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  • Sept. 30, 2016, 12:42 p.m.

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Liu, Jian & Miller, William H. Real time correlation function in a single phase spaceintegral--beyond the linearized semiclassical initial valuerepresentation, article, July 10, 2007; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc900263/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.