Capacitance and Transport through an Isolated Impurity Center in 1D Luttinger Liquid

We establish the equivalence between the problem of a solitary potential scatterer in a Luttinger liquid of spinless repulsive fermions and an anisotropic Kondo model where the value of the impurity spin id determined by the scaling dimension of the scattering potential. The Bethe ansatz is used to derive non-perturbative expressions for the capacitance and conductance.