Nonadiabatic dynamics in open quantum-classical systems: Forward-backward trajectory solution
Nonadiabatic dynamics in open quantum-classical systems: Forward-backward trajectory solution
Publication Type:
Journal ArticleSource:
Journal of Chemical Physics, Volume 137, Number 22 (2012)URL:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84871222513&doi=10.1063%2f1.4736841&partnerID=40&md5=98ad92d6e9655bb3c434fc0041402e8fKeywords:
Approximate solution, Article, Backward trajectory, Coherent state, Differential forms, Dimensional phase spaces, Dynamics, Formal solution, Liouville equation, Non-adiabatic dynamics, Phase space methods, Quantum Theory, Quantum-classical, Quantum-classical systems, time, Time evolutions, Time Factors, TrajectoriesAbstract:
A new approximate solution to the quantum-classical Liouville equation is derived starting from the formal solution of this equation in forward-backward form. The time evolution of a mixed quantum-classical system described by this equation is obtained in a coherent state basis using the mapping representation, which expresses N quantum degrees of freedom in a 2N-dimensional phase space. The solution yields a simple dynamics in which a set of N coherent state coordinates evolves in forward and backward trajectories, while the bath coordinates evolve under the influence of the mean potential that depends on these forward and backward trajectories. It is shown that the solution satisfies the differential form of the quantum-classical Liouville equation exactly. Relations to other mixed quantum-classical and semi-classical schemes are discussed. © 2012 American Institute of Physics.
