Analysis of the quantum-classical Liouville equation in the mapping basis

Journal Article · Thu Oct 07 04:00:00 EDT 2010 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3480018· OSTI ID:21559923

Nassimi, Ali; Kapral, Raymond ^[1]; Bonella, Sara ^[2]

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1. Department of Chemistry, Chemical Physics Theory Group, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)
2. Dipartimento di Fisica and CNISM Unit 1, Universita La Sapienza, P.le A. Moro 2, 00185 Rome (Italy)

The quantum-classical Liouville equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neglecting the presence of the excess coupling term on the expectation values of various types of observables. Calculations are carried out on nonadiabatic population and quantum coherence dynamics for curve crossing models. For these observables, the effects of the excess coupling term enter indirectly in the computation and good estimates are obtained with the simplified propagation.

• OSTI ID: 21559923
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 13 Vol. 133; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BOLTZMANN-VLASOV EQUATION
CALCULATION METHODS
COMPLEXES
CONSTRUCTION
DIFFERENTIAL EQUATIONS
EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
POPULATIONS
QUANTUM STATES
SIMULATION