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

We study zero-temperature spin dynamics of a particle confined to a ring in the presence of spin-orbit coupling and Ohmic electromagnetic fluctuations. We show that the dynamics of the angular position θ(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 1/2 spin do not dephase at weak dissipation but they probably decay as a power law with time at strong dissipation.