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The scattering law S(k,w) for dilute polymer solutions is obtained from Kirkwood's diffusion equation via the projection operator technique. The width Ω(k) of S(k,w) is obtained for all k without replacing the Oseen tensor by its average (as is done in the Rouse–Zimm model) using the “spring‐bead” model ignoring memory effects. For small (ka\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt N $ \end{document} ≪ 1) and large (ka ≫ 1) values of k we find Ω = 0.195 k2/β α η0 \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt N $ \end{document} and Ω = k2/βξ, respectively, indicating that the width is governed mainly by the viscosity η0 for small k values and by the friction coefficient ξ for large k values. For intermediate k values which are of importance in neutron scattering we find that in the Rouse limit Ω = k4a2/12βξ. When the hydrodynamic effects are included, Ω(k) becomes 0.055 k3/βη0. Using the Rouse–Zimm model, it is seen that the effect of pre‐averaging the Oseen tensor is to underestimate the half‐width Ω(k). The implications of the theoretical predictions for scattering experiments are discussed.

Fluctuations in nonlinear Markovian systems are studied by the Langevin equation method using system-size expansion. Langevin equations with different random sources are constructed for the description of fluctuations to varying degrees of accuracy in inverse powers of the system size ~. Evolution equations for the deterministic path, deviation of the mean from the deterministic path, and the variance are obtained in a nonstationary state in the lowest order of e. The power spectral density for fluctuations about a stable equilibrium is calculated correct to order ~2 and is compared to the exact expression for the Alkemade diode. The relaxation frequency for the decay of correlations in a critical equilibrium and the scaling law for the anomalous fluctuations are determined and compared to those obtained by Kubo et al.