Phase Memory Controls Radiative Depolarization Near an Isolated Spin Resonance

Abstract

Radiative depolarization near spin resonances in electron storage rings is conventionally described by correlated-sideband and local resonance-density theories, but a quantitative description of the crossover between them has remained lacking. Here we derive a unified finite-memory response from stochastic spin dynamics near an isolated resonance. By separating the coherent resonance contribution from stochastic fluctuations, we show that the connected correlation of the accumulated resonance-relative spin phase determines the leading off-center weak-resonance depolarization rate. Both conventional theories emerge as controlled asymptotic limits of this response, which also captures the surviving synchrotron phase memory governing the crossover. Monte Carlo spin tracking validates the predicted rates throughout the crossover and reproduces the recurrence-induced generalized-sideband structure. More broadly, the connected-correlation formulation provides a basis for extending radiative depolarization theory to more general stochastic spin-orbit dynamics in storage rings.