  We show that the Markovian dynamics of two coupled harmonic oscillators may
be analyzed using a Schr\"odinger equation and an effective non-Hermitian
Hamiltonian. This may be achieved by a non-unitary transformation that involves
superoperators; such transformation enables the removal of quantum jump
superoperators, that allows us to rewrite the Lindblad master equation in terms
of a von Neumann-like equation with an effective non-Hermitian Hamiltonian.
This may be generalized to an arbitrary number of interacting fields. Finally,
by applying an extra non-unitary transformation, we may diagonalize the
effective non-Hermitian Hamiltonian to obtain the evolution of any input state
in a fully quantum domain.
