  We use the system-plus-reservoir approach to study the quantum dynamics of a
bipartite continuous variable system (two generic particles). We present an
extension of the traditional model of a bath of oscillators which is capable of
inducing an effective coupling between the two parts of the system depending on
the choice made for the spectral density of the bath. The coupling is nonlinear
in the system variables and an exponential dependence on these variables is
imposed in order to guarantee the translational invariance of the model if the
two particles are not subject to any external potential. The reduced density
operator is obtained by the functional integral method. The dynamical
susceptibility of the reservoir is modelled in order to introduce, besides a
characteristic frequency, a characteristic length that determines if the
effective interaction potential is strong enough to induce entanglement between
the particles. Our model provides a criterion of distance for identifying in
which cases a common environment can induce entanglement. Three regimes are
found: the short distance regime, equivalent to a bilinear system-reservoir
coupling, the long distance regime in which the particles act like coupled to
independent reservoirs and the intermediate regime suitable for the competition
between decoherence and induced-entanglement.
