Analysis of the forward-backward trajectory solution for the mixed quantum-classical Liouville equation

Publication Type:

Journal Article

Authors:

Source:

Journal of Chemical Physics, Volume 138, Number 13 (2013)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84876123613&doi=10.1063%2f1.4798221&partnerID=40&md5=399b69818c2c8d8eed764c21cc070b3b

Keywords:

algorithm, Algorithms, Approximate solution, Article, Chemical, chemical model, Computer Simulation, Forward-and-backward, Large scale systems, Liouville equation, Mean-field potential, Models, Numerical tests, Quantum coherent state, Quantum process, Quantum Theory, Quantum-classical, Quantum-classical methods, Trajectories

Abstract:

Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping basis [C.-Y. Hsieh and R. Kapral, J. Chem. Phys. 137, 22A507 (2012)]10.1063/1.4736841 is one such scheme. It simulates the dynamics via the propagation of forward and backward trajectories of quantum coherent state variables, and the propagation of bath trajectories on a mean-field potential determined jointly by the forward and backward trajectories. An analysis of the properties of this solution, numerical tests of its validity and an investigation of its utility for the study of nonadiabtic quantum processes are given. In addition, we present an extension of this approximate solution that allows one to systematically improve the results. This extension, termed the jump forward-backward trajectory solution, is analyzed and tested in detail and its various implementations are discussed. © 2013 American Institute of Physics.

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