  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.
