Pseudogap Kondo Physics from Charge Fluctuations in a Quantum Dot

We consider charge fluctuations in a quantum dot coupled to an interacting one-dimensional electron liquid. We find the behavior of this system to be similar to the multichannel pseudogap Kondo model. By tuning the coupling between the dot and the one-dimensional electron liquid, one can access the quantum critical point and the various fixed points which arise. The differential capacitance is computed and is shown to contain detailed information about the system.