  The conditions under which an open quantum mechanical system may be described
by mixed quantum-classical dynamics are investigated. Decoherence is studied
using influence functional methods in a model composite quantum system
comprising two coupled systems, A and C, interacting with a harmonic bath with
Ohmic and super-Ohmic spectral densities. Subsystem A is directly coupled to
subsystem C, while C is coupled directly to the bath. Calculations are
presented for a model where subsystem A is taken to be a two-level system which
is bilinearly coupled to a single harmonic oscillator C subsystem. The loss of
quantum coherence in each subsystem is discussed in the extreme non-adiabatic
regime where the dynamics of subsystem A is essentially frozen. Subsystem C is
shown to lose its coherence rapidly, while subsystem A maintains coherence for
longer time periods since C modulates the influence of the bath on A. Thus, one
may identify situations where the coupled AC system evolution effectively obeys
mixed quantum-classical dynamics.
