II.D Scattering and Fluctuations

In addition to bulk thermodynamic experiments, scattering measurements can be used to probe microscopic fluctuations at length scales of the order of the probe wavelength λ. In a typical set up, a beam of wavevector ki is incident upon the sample and the scattered intensity is measured at wavevector ks = ki+q. For elastic scattering, |ki| = |ks| ≡ k, and q ≡ |q| = 2k sin θ, where θ is the angle between incident and scattered beams. Standard treatments of scattering start with the Fermi Golden Rule, and usually lead to a scattering amplitude of the form