The generalized quantum master equation with transport particle number resolution, similar to its conventional unconditioned counterpart, also has time-local and time-nonlocal configurations. The latter is found to be more suitable for the effect of an electrode’s bandwidth on quantum transport and noise spectrum for weak system-reservoir coupling, as calibrated with the exact results in the absence of a Coulomb interaction. We further analyze the effect of the Coulomb interaction on the noise spectrum of the transport current through quantum dot systems, and show that the realistic finite Coulomb interaction and finite bandwidth are manifested only with the non-Markovian treatment. We demonstrate a number of non-Markovian characteristics of the shot noise spectrum, including that which is due to finite bandwidth and that which is sensitive to and enhanced by the magnitude of the Coulomb interaction.

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