  We study zero temperature spin dynamics of a particle confined to a ring in
presence of spin orbit coupling and Ohmic electromagnetic fluctuations. We show
that the dynamics of the angular position $\theta(t)$ are decoupled from the
spin dynamics and that the latter is mapped to certain correlations of a
spinless 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. The
parallel (in plane) components for spin $\half$ do not dephase at weak
dissipation but they probably decay as a power law with time at strong
dissipation.
