  Master equations are commonly used to describe time evolution of open
systems. We introduce a general method for calculating a Markovian solution of
the Nakajima-Zwanzig generalized master equation. We do so for a time dependent
transport of interacting electrons through a complex nano scale system in a
photon cavity. The central system, described by 120 many-body states in a Fock
space, is weakly coupled to the external leads. The very diverse relaxation
times of the open system, reflecting radiative or non-radiative transitions,
require information about the time evolution through many orders of magnitude.
In our approach, the generalized master equation is mapped from a many-body
Fock space of states to a Liouville space of transitions. We show that this
results in a linear equation which is solved exactly through an eigenvalue
analysis, which supplies information on the steady state and the time evolution
of the system.
