From quantum critical to two-channel Kondo physics via charge fluctuations in a quantum dot

We consider charge fluctuations in a quantum dot coupled to an interacting one-dimensional electron liquid. By tuning the coupling between the dot and the one-dimensional electron liquid, one can access the various regimes which arise, which include a quantum critical and a two-channel Kondo regime. The differential capacitance is computed and is shown to contain detailed information about the system.