  In this paper it is studied the influence of a minimal thermal environment on
the dynamics of a quantum harmonic oscillator (labelled A), prepared in a
coherent state. The environment itself consists of a second oscillator
(labelled B), initially in a thermal state. Two types of interaction
Hamiltonians are considered, and the time-evolution of the reduced density
operator of oscillator A is compared to the one obtained from the usual master
equation approach, i.e., assuming that oscillator A is coupled to a large
reservoir. An analysis of the linear entropy evolution of oscillator A shows
that simplified models may be able to describe important features related to
the phenomenon of decoherence.
