Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

doi:10.1063/1.4961551

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

Journal Article · Sun Aug 28 04:00:00 EDT 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4961551· OSTI ID:22678928

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

OSTI ID:: 22678928

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 8 Vol. 145; ISSN JCPSA6; ISSN 0021-9606

Country of Publication:: United States

Language:: English

References (11)

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A Symmetrical Quasi-Classical Spin-Mapping Model for the Electronic Degrees of Freedom in Non-Adiabatic Processes Cotton, Stephen J.; Miller, William H. The Journal of Physical Chemistry A, Vol. 119, Issue 50 https://doi.org/10.1021/acs.jpca.5b05906	journal	August 2015
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Two-dimensional vibronic spectra from classical trajectories Polley, Kritanjan; Loring, Roger F. The Journal of Chemical Physics, Vol. 150, Issue 16 https://doi.org/10.1063/1.5093911	journal	April 2019
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Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy Li, Tao E.; Nitzan, Abraham; Sukharev, Maxim Physical Review A, Vol. 97, Issue 3 https://doi.org/10.1103/physreva.97.032105	journal	March 2018
Performance Evaluation of the Symmetrical Quasi-Classical Dynamics Method based on Meyer-Miller Mapping Hamiltonian in the Treatment of Site-Exciton Models Xie, Yu; Zheng, Jie; Lan, Zhenggang arXiv https://doi.org/10.48550/arxiv.1807.01818	text	January 2018

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