  We carry out a detailed analysis of coherent resonant tunneling through two
coupled quantum dots (CQD) in a parallel arrangement in the weak tunneling
limit. We establish a set of quantum rate equations (QREs) in terms of the
eigenstate-representation by means of a generic quantum Langevin equation
approach, which is valid for arbitrary bias-voltage, temperature, and interdot
hopping strength. Based on linear-response theory, we further derive the
current and frequency-independent shot noise formulae. Our results reveal that
a previously used formula for evaluating Schottky-type noise of a "classical"
single-electron transistor is a direct result of linear-response theory, and it
remains applicable for small quantum devices with internal coupling. Our
numerical calculations show some interesting transport features (i) for a
series-CQD: the appearance of a NDC due to the bias-voltage-induced shifting of
bare levels or a finite interdot Coulomb repulsion, and (ii) for a parallel CQD
in strong interdot Coulomb repulsion regime: finite-bias-induced AB
oscillations of current, and magnetic-flux-controllable negative differential
conductance and a huge Fano factor.
