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Persistent currents in quantum phase slip rings

We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current and the critical radius of the ring beyond which this current gets exponentially suppressed by quantum fluctuations. We also analyze fluctuations of persistent current caused by quantum phase slips. At low temperatures the supercurrent noise spectrum has the form of coherent peaks which can be tuned by the magnetic flux. Experimental observation of these peaks can directly demonstrate the existence of plasma modes in superconducting nanorings.