  A weak coupling quantum master equation provides reliable steady-state
results only in the van Hove limit, i.e., when the system-lead coupling
approaches zero. Recently, J. Thingna et al. [Phys. Rev. E 88, 052127 (2013)]
proposed an alternative approach, based on an analytic continuation of the
Redfield solution, to evaluate the reduced density matrix up to second order in
the system-bath coupling. The approach provides accurate results for harmonic
oscillator and spin-bosonic systems. We apply this approach to study fermionic
systems and the calculation on an exactly solvable double quantum dot system
shows that the method is rigorously valid only near equilibrium, i.e., linear
response regime. We further compare to the Redfield and the secular Redfield
(Lindblad-type) master equations that are inaccurate in all parameter regimes.
Lastly, we consider the non-trivial problem of strong Coulomb interaction and
illustrate the interplay between system-lead coupling, inter-dot tunneling, and
Coulomb strength that can be captured only via the analytic continuation
method.
