We develop a Luttinger-liquid theory of the Coulomb drag of persistent currents flowing in concentric mesoscopic rings by incorporating nonlinear corrections to the electron dispersion relation. We demonstrate that at low temperatures, interactions between electrons in different rings generate an additional phase and thus alter the period of Aharonov-Bohm oscillations. The resulting nondissipative drag depends strongly on the relative parity of the electron numbers. We also show that interactions set a new temperature scale below which the linear response theory does not apply at certain values of external flux.
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Shahbazyan et al. (1997) studied this question.