  The equilibrium properties of an open harmonic oscillator are considered in
three steps: First the creation and destruction operators are generalized for
open dynamics and the creation operator is used to construct coherent states.
The second step consists of the introduction of the Heisenberg representation
where the dynamical decoherence can be identified without making reference to
the state of the system. Finally it is pointed out that the quantum
fluctuations generate non-continuous limit for infinitesimal system-environment
interactions and at the border of the under- and over-damped oscillator.
