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