  We demonstrate that with a stepwise introduction of complexity to a model of
an electron system embedded in a photonic cavity and a carefully controlled
stepwise truncation of the ensuing many-body space it is possible to describe
the time-dependent transport of electrons through the system with a
non-Markovian generalized quantum master equation. We show how this approach
retains effects of an external magnetic field and the geometry of an
anisotropic electronic system. The Coulomb interaction between the electrons
and the full electromagnetic coupling between the electrons and the photons are
treated in a non-perturbative way using "exact numerical diagonalization".
