Decoherence and Quantum-Classical Master Equation Dynamics

Details Decoherence and Quantum-Classical Master Equation Dynamics Decoherence and Quantum-Classical Master Equation Dynamics

2006-12-07

arxiv.org/abs/cond-mat/0612203v2

Physics

Condensed Matter

Statistical Mechanics

13 pages, 6 figures, revision includes: Added references on mixed quantum-classical Liouville theory, and some minor details t

Scientific paper

The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still non-Markovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of non-equilibrium average values or correlation functions is considered, the non-Markovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a model nonadiabatic chemical reaction.

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