Kondo tunneling tgrough a biased quantum dot

Electron tunneling through a system formed by two coupled quantum dots in a parallel geometry is considered within a generalized Anderson model. The dots are assumed to have nearly equal radii but different (and tunable) gate voltages. In the absence of tunneling to and from the leads, the isolated two-dot system (with two electrons in it) resembles an hydrogen molecule within the Heitler London approximation. In particular, it has a singlet ground state and low lying excited triplet state. When tunneling is switched on, and when the gate voltages are properly tuned the ground state becomes a triplet and singlet and triplet states are intermixed. In the region where charge fluctuations are suppressed, the pertinent antiferromagnectic exchange interaction has the form $(J^{T} {\bf S} +J^{ST} {\bf P}) \cdot {\bf s}$. It is written in terms of the electron spin ${\bf s}$, the double dot spin 1 operator ${\bf S}$ and an additional vector operator ${\bf P}$. The operators ${\bf S}$ and ${\bf P}$ generate the algebra $o_{4}$ of a spin rotator. The related Kondo effect is similar to that of a vertical quantum dot, discussed and analyzed recently.