Relationship between the noise-induced persistent current and the dephasing rate

ac noise in disordered conductors causes both dephasing of the electron wave functions and 1 dc current around a mesoscopic ring. We demonstrate that the dephasing rate tau(phi)(-1) in long wires and the de current < I >, induced by the same noise and averaged over an ensemble of small rings, are connected in a remarkably simple way: < I >tau(phi) = C(beta)e. Here e is an electron charge. and the constant C-beta similar to 1 depends on the Dyson symmetry class. The relationship seems to agree reasonably with experiments. This suggests that the two puzzles, anomalously large persistent current and the low-temperature saturation of the dephasing, may have a common solution.