Stationary spectrum of a linear fluctuating interface
= Stationary spectrum of a linear fluctuating interface
{title2=$\langle h_q^2\rangle=\sigma^2/(2\alpha q^2)$}
For a nonzero <Fourier mode> satisfying $dh_q=-\alpha q^2h_q\,dt+\sigma\,dW_q$ with $\alpha>0$, the <explicit Ornstein-Uhlenbeck solution> and <Itô isometry> give the stationary <second moment> $\sigma^2/(2\alpha q^2)$. The prefactor depends on the normalization of the mode noise, while the inverse-square dependence follows from diffusive relaxation.