Exact eigenstates and transmission for two interacting electrons on quantum dots

The eigenstates and the scattering transmission for two interacting electrons are found exactly for I quantum dots, including the hybridization with the states on the leads. The results imply limitations on the validity of the Coulomb blockade picture. The ground states for I=1, and 2 on a one--dimensional chain (modeling single and double quantum dots) exhibit quantum delocalization and magnetic transitions. The effective transmission T of two interacting electrons through one impurity (I=1) is enhanced by a renormalization of the repulsive interaction, when one of the electrons is captured in a strongly localized state.