Capacitance of a resonant level coupled to Luttinger liquids

In this paper we study the differential capacitance of a single-level quantum dot attached to quantum wires in the Luttinger liquid phase, or to fractional quantum Hall edges, by both tunneling and interactions. We show that logarithmic or even power-law divergence of the capacitance at low temperatures may result in a substantial region of the parameter space (including the $\nu =1\mathrm{/}3$ filling). This behavior is a manifestation of generalized two channel Kondo physics, and can be used to extract Luttinger liquid parameters from thermodynamic measurements.