Mixed quantum-classical dynamics

Publication Type:

Journal Article

Authors:

Source:

Journal of Chemical Physics, American Institute of Physics Inc., Volume 110, Number 18, p.8919-8929 (1999)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-0001385642&doi=10.1063%2f1.478811&partnerID=40&md5=ce3e6a4dd5a2a26d7a65452fab03625a

Keywords:

Coupled evolution, Diagonal elements, Equation of motion, Equations of motion, Liouville equation, Mixed quantum-classical dynamics, Projection-operator method, Quantum electronics, Quantum optics, Quantum subsystems, Quantum-classical, Wigner transforms

Abstract:

Mixed quantum-classical equations of motion are derived for a quantum subsystem of light (mass in) particles coupled to a classical bath of massive (mass M) particles. The equation of motion follows from a partial Wigner transform over the bath degrees of freedom of the Liouville equation for the full quantum system, followed by an expansion in the small parameter μ = (m/M)1/2 in analogy with the theory of Brownian motion. The resulting mixed quantum-classical Liouville equation accounts for the coupled evolution of the subsystem and bath. The quantum subsystem is represented in an adiabatic (or other) basis and the series solution of the Liouville equation leads to a representation of the dynamics in an ensemble of surface-hopping trajectories. A generalized Pauli master equation for the evolution of the diagonal elements of the density matrix is derived by projection operator methods and its structure is analyzed in terms of surface-hopping trajectories. © 1999 American Institute of Physics.