Coulomb Blockade-Effects on Quantization of Charge and Persistent Current in a Luttinger-Liquid Ring

We show that in a ring-shaped Luttinger Liquid (LL) in contact with an electron reservoir --- the chemical potential in the ring being controlled by a gate voltage $V_g$ --- both the average ring charge and the persistent current in the ring are step-like functions of $V_g$ at low temperatures. The step positions are determined by the LL parameter $\alpha=v_F/s$, which therefore can be directly measured. We study electrons both with and without spin, taking into account long-range interactions in the ring.