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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 · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4961551· OSTI ID:1379579
 [1];  [2]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry, Kenneth S. Pitzer Center for Theoretical Chemistry
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemcial Sciences Division
+ Show Author Affiliations
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.
Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1379579
Alternate ID(s):
OSTI ID: 1328640
OSTI ID: 22678928
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 8 Vol. 145; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

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The Symmetrical Quasi-Classical Model for Electronically Non-Adiabatic Processes Applied to Energy Transfer Dynamics in Site-Exciton Models of Light-Harvesting Complexes journal February 2016
A Symmetrical Quasi-Classical Spin-Mapping Model for the Electronic Degrees of Freedom in Non-Adiabatic Processes journal August 2015
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Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electronically non-adiabatic processes journal December 2013
Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electron transfer journal August 2014
Communication: Note on detailed balance in symmetrical quasi-classical models for electronically non-adiabatic dynamics journal April 2015
On the Quantum Correction For Thermodynamic Equilibrium journal June 1932

Cited By (16)

Classical molecular dynamics simulation of electronically non-adiabatic processes journal January 2016
A new symmetrical quasi-classical model for electronically non-adiabatic processes: Application to the case of weak non-adiabatic coupling journal October 2016
Multi-state trajectory approach to non-adiabatic dynamics: General formalism and the active state trajectory approximation journal July 2017
On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics journal August 2017
Communication: Symmetrical quasi-classical analysis of linear optical spectroscopy journal May 2018
The symmetrical quasi-classical approach to electronically nonadiabatic dynamics applied to ultrafast exciton migration processes in semiconducting polymers journal July 2018
Performance evaluation of the symmetrical quasi-classical dynamics method based on Meyer-Miller mapping Hamiltonian in the treatment of site-exciton models journal November 2018
A symmetrical quasi-classical windowing model for the molecular dynamics treatment of non-adiabatic processes involving many electronic states journal March 2019
Two-dimensional vibronic spectra from classical trajectories journal April 2019
Trajectory-adjusted electronic zero point energy in classical Meyer-Miller vibronic dynamics: Symmetrical quasiclassical application to photodissociation journal May 2019
State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics journal June 2019
Nonadiabatic simulation of singlet fission dynamics in tetracene clusters: The topology of quantum coherence in a global view journal August 2019
A new perspective for nonadiabatic dynamics with phase space mapping models journal July 2019
Combining the mapping Hamiltonian linearized semiclassical approach with the generalized quantum master equation to simulate electronically nonadiabatic molecular dynamics journal August 2019
Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy 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 text January 2018

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