Numerical calculations are shown to reproduce the main results of recent experiments involving nonlocal spin control in nanostructures (N. J. Craig et al., Science 304, 565 (2004)). In particular, the splitting of the zero-bias-peak discovered experimentally is clearly observed in our studies. To understand these results, a simple "circuit model" is introduced and shown to provide a good qualitative description of the experiments. The main idea is that the splitting originates in a Fano anti-resonance, which is caused by having one quantum dot side-connected in relation to the current's path. This scenario provides an explanation of Craig et al.'s results that is alternative to the RKKY proposal, which is here also addressed.

The conductance of two interacting dots connected to leads is studied. The configuration is such that one dot is embedded into the leads while the other is tunneling-coupled only to the first dot. The effect of the tunneling interaction strength on the conductance is discussed. As the two dot levels cross the Fermi level the low temperature conductance of the system cancels out, due to interference effects. This cancellation persists over a range of gate potential that depends upon the interaction strength: the greater the interaction the larger the range of gate potential where the current vanishes.

The conductance of a double-dot system in a ring threaded by a magnetic flux is studied. The ring is connected to two leads in such a way that each dot is embedded in one arm of the structure. The currents going through each arm of the ring are determined by the Aharonov-Bohm effect and the dot charging effects. The conductance for different values of the magnetic flux is obtained as a function of the gate potentials applied to the dots, for two situations: when the dot level energies are equal, deltaE = 0, and when they are different but with deltaE smaller than the Coulomb interaction U. The conductance shows quite distinct behavior according to having a finite or zero magnetic flux threading the ring. The system presents S = 1/2 and S = 1 Kondo phenomena for no magnetic flux and is in the S = 1/2 Kondo regime in the case of half a quantum of magnetic flux.