Intrawell phase autocorrelation (source code)

= Intrawell phase autocorrelation
{title2=$C(\tau)\simeq\alpha^2+(T_{\rm eff}/\kappa)e^{-\kappa|\tau|}$}

Near the stable <Adler phase equation> point $\alpha=\arcsin(\omega/\epsilon)$, linearized noise obeys an <Ornstein-Uhlenbeck process> with relaxation rate $\kappa=\sqrt{\epsilon^2-\omega^2}$. Its harmonic-model raw correlation is $\alpha^2+(T_{\rm eff}/\kappa)e^{-\kappa|\tau|}$. Nonlinear drift also shifts the local mean at order $T_{
m eff}$. 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.