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

TL;DR

This paper investigates zero temperature spin dynamics of a particle on a ring with spin-orbit coupling and Ohmic noise, revealing that certain spin components do not dephase over time.

Contribution

It demonstrates that spin dynamics can be decoupled from angular motion and maps spin correlations to a spinless particle model, providing new insights into spin coherence under environmental noise.

Findings

Long-time finiteness of perpendicular spin correlations.

Parallel spin components do not dephase at weak dissipation.

Possible power-law decay of in-plane spin components at strong dissipation.

Abstract

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.