Subsystem dynamics in mixed quantum-classical systems

Starting with the mixed quantum-classical Liouville equation, projection op erator methods are used to derive an equation of motion for a quantum subsy stem dissipatively interacting with a classical bath. The resulting general ized master equation is reduced to the Lindblad equation after making a Mar kovian approximation in the weak coupling limit. The bath subsystem dynamic s is studied from a similar perspective. For situations where the classical subsystem consists of few degrees of freedom, or one is interested in the nature of the modifications of its dynamics as a result of coupling to a la rge, rapidly relaxing quantum bath, a classical analog of the Lindblad equa tion is derived and discussed. (C) 2001 Elsevier Science B.V. All rights re served.