Higher-order results for the relation between channel conductance and the Coulomb blockade for two tunnel-coupled quantum dots

We extend earlier results on the relation between the dimensionless tunneling channel conductance g and the fractional Coulomb-blockade peak splitting f for two electrostatically equivalent dots connected by an arbitrary number N-ch of tunneling channels with bandwidths W much larger than the two-dot differential charging energy U-2. By calculating f through the second order in g in the limit of weak coupling (g-->0), we illuminate the difference in behavior of the large-N-ch and small-N-ch regimes and make more plausible extrapolation to the strong-coupling (g-->1) limit. For the special case of N-ch=2 and strong coupling, we eliminate an apparent ultraviolet divergence and obtain the next leading term of an expansion in (1-g). We show that the results we calculate are independent of such band structure details as the fraction of occupied fermionic single-particle states in the weak-coupling theory and the nature of the cutoff in the bosonized strong-coupling theory. The results agree with calculations for metallic junctions in the N-ch-->infinity limit and improve the previous good agreement with recent two-channel experiments.