Speckle from phase ordering systems

The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a nonconserved, scalar order parameter (Model A), quenched through an order-disorder transition into the two-phase regime. For such systems it is well established that the standard scaling hypothesis applies, consequently the average scattering intensity at wavevector _k and time t' is proportional to a scaling function which depends only on a rescaled time, t ~ |_k|^2 t'. We find that the simulated intensities are exponentially distributed, with the time-dependent average well approximated using a scaling function due to Ohta, Jasnow, and Kawasaki. Considering fluctuations around the average behavior, we find that the covariance of the scattering intensity for a single wavevector at two different times is proportional to a scaling function with natural variables mt = |t_1 - t_2| and pt = (t_1 + t_2)/2. In the asymptotic large-pt limit this scaling function depends only on z = mt / pt^(1/2). For small values of z, the scaling function is quadratic, corresponding to highly persistent behavior of the intensity fluctuations. We empirically establish a connection between the intensity covariance and the two-time, two-point correlation function of the order parameter. This connection allows sensitive testing, either experimental or numerical, of existing theories for two-time correlations in systems undergoing order-disorder phase transitions. Comparison between theory and our numerical results requires no adjustable parameters.