  We analyze fluctuations of persistent current (PC) produced by a charged
quantum particle moving in a ring and interacting with a dissipative
environment formed by diffusive electron gas. We demonstrate that in the
presence of interactions such PC fluctuations persist down to zero temperature.
In the case of weak interactions and/or sufficiently small values of the ring
radius $R$ PC noise remains coherent and can be tuned by external magnetic flux
$\Phi_x$ piercing the ring. In the opposite limit of strong interactions and/or
large values of $R$ fluctuations in the electronic bath strongly suppress
quantum coherence of the particle down to $T=0$ and induce incoherent
$\Phi_x$-independent current noise in the ring which persists even at
$\Phi_x=0$ when the average PC is absent.
