Intrawell phase autocorrelation ($C(\tau )\simeq {\alpha }^2+(T_{\mathrm{eff}}/\kappa )e^{-\kappa |\tau |}$)

Near the stable Adler phase equation point $\alpha =\arcsin (\omega /ϵ)$, linearized noise obeys an Ornstein-Uhlenbeck process with relaxation rate $\kappa =\sqrt{{ϵ}^2-{\omega }^2}$. Its harmonic-model raw correlation is ${\alpha }^2+(T_{\mathrm{eff}}/\kappa )e^{-\kappa |\tau |}$. Nonlinear drift also shifts the local mean at order $T_{meff}$. This describes times after relaxation but before appreciable phase slips; it is not a stationary infinite-time correlation of the unwrapped phase at fixed nonzero noise.