Numerical simulations of scattering speckle from phase ordering systems

TL;DR

This paper presents large-scale simulations of speckle pattern dynamics in a phase ordering system, revealing how the correlation decay time scales with wave vector and time, aiding understanding of scattering in evolving systems.

Contribution

It extends the scaling hypothesis to the two-time correlation function of scattering intensity in phase ordering systems, providing new insights into speckle dynamics.

Findings

Intensity at each wave vector is exponentially distributed.

Correlation decay time scales as k times the square root of the sum of times.

Speckle fluctuations can be characterized by the extended scaling hypothesis.

Abstract

The scattering of coherent X-rays from dynamically evolving systems is currently becoming experimentally feasible. The scattered beam produces a pattern of bright and dark speckles, which fluctuate almost independently in time and can be used to study the dynamics of the system. Here we report large-scale computer simulations of the speckle dynamics for a phase ordering system, using a two-dimensional model quenched through an order--disorder transition into the two-phase regime. The intensity at each wave vector ${\bf k}$ is found to be an exponentially distributed random variable. The scaling hypothesis is extended to the two-time correlation function of the scattering intensity at a given wave vector, $Corr({\bf k};t_1,t_2)$. The characteristic decay time difference for the correlation function, $|t_1 - t_2|_c$, is found to scale as $k|t_1 + t_2|^{1/2}$.