  A novel method based on spectral Green functions is presented for the
simulation of driven open quantum dynamics that can be described by the
Lindblad master equation in Liouville density operator space. The method
extends the Hilbert space formalism and provides simple algebraic connections
between the driven and non-driven dynamics in the spectral frequency domain.
The formalism shows remarkable analogies to the use of Green functions in
quantum field theory such as the elementary excitation energies and the Dyson
self-energy equation. To demonstrate its potential, we apply the novel method
to a coherently driven dissipative ensemble of 2-level systems comprising a
single "active" subsystem interacting with $N$ "passive" subsystems -- a
generic model with important applications in quantum optics and dynamic nuclear
polarization. The novel method dramatically reduces computational cost compared
with simulations based on solving the full master equation, thus making it
possible to study and optimize many-body correlated states in the physically
realistic limit of an arbitrarily large $N$.
