  Conductance, on-site and inter-site charge fluctuations and spin correlations
in the system of two side-coupled quantum dots are calculated using the
Wilson's numerical renormalization group (NRG) technique. We also show spectral
density calculated using the density-matrix NRG, which for some parameter
ranges remedies inconsistencies of the conventional approach. By changing the
gate voltage and the inter-dot tunneling rate, the system can be tuned to a
non-conducting spin-singlet state, the usual Kondo regime with odd number of
electrons occupying the dots, the two-stage Kondo regime with two electrons, or
a valence-fluctuating state associated with a Fano resonance. Analytical
expressions for the width of the Kondo regime and the Kondo temperature are
given. We also study the effect of unequal gate voltages and the stability of
the two-stage Kondo effect with respect to such perturbations.
