  The dynamical invariant, whose expectation value is constant, is generalized
to open quantum system. The evolution equation of dynamical invariant (the
dynamical invariant condition) is presented for Markovian dynamics. Different
with the dynamical invariant for the closed quantum system, the evolution of
the dynamical invariant for the open quantum system is no longer unitary, and
the eigenvalues of it are time-dependent. Since any hermitian operator
fulfilling dynamical invariant condition is a dynamical invariant, we propose a
sort of special dynamical invariant (decoherence free dynamical invariant) in
which a part of eigenvalues are still constant. The dynamical invariant in the
subspace spanned by the corresponding eigenstates evolves unitarily. Via the
dynamical invariant condition, the results demonstrate that this dynamical
invariant exists under the circumstances of emergence of decoherence free
subspaces.
