Spectroscopy of the Kondo Problem in a Box

We study the spin quantum numbers and energy eigenvalues of the ground state and low lying excitations of a quantum dot with a single spin-S impurity. We prove an exact theorem that allows us to infer the ground state spin for an arbitrary spin-S of the impurity and for even/odd electrons on the quantum dot. Additionally, strong and weak coupling perturbation theory backed up with quantum Monte-Carlo simulations enable us to map out the spin structure of the excited states and the energy splittings between them as the ratio $\Delta/T_K $ is tuned. We propose a simple transport experiment involving the tunneling spectroscopy of a double quantum dot, where these results can be observed. Finally, we make explicit contact with experiment by calculating the transport properties of the proposed double dot device that exhibit signatures of tunneling into the Kondo-correlated state.