  We theoretically analyze equilibrium fluctuations of persistent current (PC)
in nanorings. We demonstrate that these fluctuations persist down to zero
temperature provided the current operator does not commute with the total
Hamiltonian of the system. For a model of a quantum particle on a ring we
explicitly evaluate PC noise power which has the form of sharp peaks at
frequencies set by the corresponding interlevel distances. In rings with many
conducting channels a much smoother and broader PC noise spectrum is expected.
A specific feature of PC noise is that its spectrum can be tuned by an external
magnetic flux indicating the presence of quantum coherence in the system.
