Analysis of the quantum-classical Liouville equation in the mapping basis
- 6 October 2010
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 133 (13), 134115
- https://doi.org/10.1063/1.3480018
Abstract
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 coherencedynamics 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.Keywords
This publication has 44 references indexed in Scilit:
- Mapping approach for quantum-classical time correlation functionsCanadian Journal of Chemistry, 2009
- Trotter-Based Simulation of Quantum-Classical DynamicsThe Journal of Physical Chemistry B, 2007
- PROGRESS IN THE THEORY OF MIXED QUANTUM-CLASSICAL DYNAMICSAnnual Review of Physical Chemistry, 2006
- Nonadiabatic Dynamics of Condensed Phase Rate ProcessesAccounts of Chemical Research, 2005
- Mixed quantum-classical dynamicsThe Journal of Chemical Physics, 1999
- Mapping approach to the semiclassical description of nonadiabatic quantum dynamicsPhysical Review A, 1999
- Simulation of Coherent Nonadiabatic Dynamics Using Classical TrajectoriesThe Journal of Physical Chemistry A, 1998
- Dynamics by Semiclassical MethodsAnnual Review of Physical Chemistry, 1994
- Molecular dynamics with electronic transitionsThe Journal of Chemical Physics, 1990
- Classical trajectory model for electronically nonadiabatic collision phenomena. A classical analog for electronic degrees of freedomThe Journal of Chemical Physics, 1978