  Employing instanton technique we evaluate equilibrium persistent current (PC)
produced by a quantum particle moving in a periodic potential on a ring and
interacting with a dissipative environment formed by diffusive electron gas.
The model allows for detailed non-perturbative analysis of interaction effects
and -- depending on the system parameters -- yields a rich structure of
different regimes. We demonstrate that at low temperatures PC is exponentially
suppressed at sufficiently large ring perimeters $2\pi R> L_{\varphi}$ where
the dephasing length $L_{\varphi}$ is set by interactions and does not depend
on temperature. This behavior represents a clear example of quantum decoherence
by electron-electron interactions at $T\to 0$.
