  In the framework of the Heisenberg picture, an alternative derivation of the
reduced density matrix of a driven dissipative quantum harmonic oscillator as
the prototype of an open quantum system is investigated. The reduced density
matrix for different initial states of the combined system is obtained from a
general formula, and different limiting cases are studied. Exact expressions
for the corresponding characteristic function in quantum thermodynamics and
Wigner quasi distribution function are found. A possible generalization based
on the Magnus expansion of the evolution operator is presented.
