A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems
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.
- Authors:
-
- Institute for Computational Engineering and Sciences and Department of Chemistry, University of Texas at Austin, Austin, Texas 78712 (United States)
- Physical Chemistry, Department of Chemistry and Molecular Biology, University of Gothenburg, SE 41296 Gothenburg (Sweden)
- Publication Date:
- OSTI Identifier:
- 22490831
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 24; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; CORRELATION FUNCTIONS; DENSITY; MOLECULAR DYNAMICS METHOD; PATH INTEGRALS
Citation Formats
Smith, Kyle K. G.,, Poulsen, Jens Aage, E-mail: jens72@chem.gu.se, Nyman, Gunnar, and Rossky, Peter J., E-mail: Peter.Rossky@rice.edu. A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems. United States: N. p., 2015.
Web. doi:10.1063/1.4922887.
Smith, Kyle K. G.,, Poulsen, Jens Aage, E-mail: jens72@chem.gu.se, Nyman, Gunnar, & Rossky, Peter J., E-mail: Peter.Rossky@rice.edu. A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems. United States. https://doi.org/10.1063/1.4922887
Smith, Kyle K. G.,, Poulsen, Jens Aage, E-mail: jens72@chem.gu.se, Nyman, Gunnar, and Rossky, Peter J., E-mail: Peter.Rossky@rice.edu. 2015.
"A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems". United States. https://doi.org/10.1063/1.4922887.
@article{osti_22490831,
title = {A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems},
author = {Smith, Kyle K. G., and Poulsen, Jens Aage, E-mail: jens72@chem.gu.se and Nyman, Gunnar and Rossky, Peter J., E-mail: Peter.Rossky@rice.edu},
abstractNote = {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.},
doi = {10.1063/1.4922887},
url = {https://www.osti.gov/biblio/22490831},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 24,
volume = 142,
place = {United States},
year = {Sun Jun 28 00:00:00 EDT 2015},
month = {Sun Jun 28 00:00:00 EDT 2015}
}