Persistent current noise in normal and superconducting nanorings

We investigate fluctuations of persistent current (PC) in nanorings both with and without dissipation and decoherence. We demonstrate that such PC fluctuations may persist down to zero temperature provided there exists either interaction with an external environment or an external (periodic) potential produced, e.g., by quantum phase slips in superconducting nanorings. Provided quantum coherence is maintained in the system PC noise remains coherent and can be tuned by an external magnetic flux $\Phi_x$ piercing the ring. If quantum coherence gets suppressed by interactions with a dissipative bath PC noise becomes incoherent and $\Phi_x$-independent.