  Motivated by activities of several experimental groups we investigate
electron transport through two coherent, strongly coupled quantum dots ("double
quantum dots"), taking into account both intra- and inter-dot Coulomb
interactions. The shot noise in this system is very sensitive to the internal
electronic level structure of the coupled dot system and its specific coupling
to the electrodes. Accordingly a comparison between experiments and our
predictions should allow for a characterization of the relevant parameters. We
discuss in detail the effect of asymmetries, either asymmetries in the
couplings to the electrodes or a detuning of the quantum dot levels out of
resonance with each other. In the Coulomb blockade region super-Poissonian
noise appears even for symmetric systems. For bias voltages above the
sequential tunneling threshold super-Poissonian noise and regions of negative
differential conductance develop if the symmetry is broken sufficiently
strongly.
