  We consider a particle in the approximation of a harmonic oscillator, coupled
linearly to a field modeling an environment. The field is described by an
infinite set of harmonic oscillators, and the system (particle--field) is
considered in a cavity at thermal equilibrium. We employ the notions of bare
and dressed coordinates to study the time evolution of the occupation number.
With dressed coordinates no renormalization procedure is required, leading
directly to a finite result. In particular, for a large time, the occupation
number of the particle becomes independent of its initial value. So we have a
Markovian process, describing the particle thermalization with the environment.
