Thermodynamic method of detecting Luttinger-liquid behavior in a one-dimensional ring of electrons

We propose a method to detect a Luttinger liquid (LL)-like behavior of a quasi-one-dimensional ring of electrons that does not depend on a transport measurement. Rather, a Coulomb blockade-induced quantization of the persistent current and excess charge in a ring of interacting electrons are shown to depend on the interaction strength. Both the average ring charge and the persistent current are step-like functions of an applied gate voltage at low temperatures. The step positions are determined by the LL parameter alpha, which therefore can be directly measured.