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We study zero temperature spin dynamics of a particle confined to a ring inpresence of spin orbit coupling and Ohmic electromagnetic fluctuations. We showthat the dynamics of the angular position $\theta(t)$ are decoupled from thespin dynamics and that the latter is mapped to certain correlations of aspinless particle. We find that the spin correlations in the $z$ direction(perpendicular to the ring) are finite at long times, i.e. do not dephase. Theparallel (in plane) components for spin $\half$ do not dephase at weakdissipation but they probably decay as a power law with time at strongdissipation.

Zero temperature geometric spin dephasing on a ring in presence of an Ohmic environment