  We study steady state transport through a double quantum dot array using the
equation-of-motion approach to the nonequilibrium Green functions formalism.
This popular technique relies on uncontrolled approximations to obtain a
closure for a hierarchy of equations, however its accuracy is questioned. We
focus on 4 different closures, 2 of which were previously proposed in the
context of the single quantum dot system (Anderson impurity model) and were
extended to the double quantum dot array, and develop 2 new closures. Results
for the differential conductance are compared to those attained by a master
equation approach known to be accurate for weak system-leads couplings and high
temperatures. While all 4 closures provide an accurate description of the
Coulomb blockade and other transport properties in the single quantum dot case,
they differ in the case of the double quantum dot array, where only one of the
developed closures provides satisfactory results.This is rationalized by
comparing the poles of the Green functions to the exact many-particle energy
differences for the isolate system. Our analysis provides means to extend the
equation-of-motion technique to more elaborate models of large bridge systems
with strong electronic interactions.
