  The interplay between interference effects and electron-electron interactions
in electron transport through an interacting double quantum dot system is
investigated using a hierarchical quantum master equation approach which
becomes exact if carried to infinite order and converges well if the
temperature is not too low. Decoherence due to electron-electron interactions
is found to give rise to pronounced negative differential resistance, enhanced
broadening of structures in current-voltage characteristics and an inversion of
the electronic population. Dependence on gate voltage is shown to be a useful
method of distinguishing decoherence-induced phenomena from effects induced by
other mechanisms such as the presence of a blocking state. Comparison of
results obtained by the hierarchical quantum master equation approach to those
obtained from the Born-Markov approximation to the Nakajima-Zwanzig equation
and from the non-crossing approximation to the nonequilibrium Green's function
reveals the importance of an inter-dot coupling that originates from the energy
dependence of the conduction bands in the leads and the need for a systematic
perturbative expansion.
