  Based on a Liouville-space formulation of open systems, we present two
methods to solve the quantum dynamics of coupled harmonic oscillators
experiencing Markovian loss. Starting point is the quantum master equation in
Liouville space which is generated by a Liouvillian that induces a Lie algebra.
We show how this Lie algebra allows to define ladder operators that construct
Fock-like eigenstates of the Liouvillian. These eigenstates are used to
decompose the time-evolved density matrix and, together with the accompanying
eigenvalues, provide insight into the transport properties of the lossy system.
Additionally, a Wei-Norman expansion of the generated time evolution can be
found by a structure analysis of the algebra. This structure analysis yields a
construction principle to implement effective non-Hermitian Hamiltonians in
lossy systems.
