  Through a set of generators that preserves the hermiticity and trace of
density matrices, we analyze the damping of harmonic oscillator in open quantum
systems into four modes, distinguished by their specific effects on the
covariance matrix of position and momentum of the oscillator. The damping modes
could either cause exponential decay to the initial covariance matrix or shift
its components. They have to act together properly in actual dynamics to ensure
that the generalized uncertainty relation is satisfied. We use a few quantum
master equations to illustrate the results.
