Defect Annihilation in Liquid Crystal Physics: Using Deep Learning to Probe the Dynamics of Defects

Smectic liquid crystals are a fluid state of matter that supports long-lived topological defects. Classical defect annihilation dynamics in two dimensions are well described by the XY-model, which predicts dynamical scaling—a single length scale controlling the dynamics. Despite years of diligent experimentation by the community, the applicability of the XY model to the defect dynamics in liquid crystals remains an open question. Recent theoretical and experiment investigations on the dynamics of isolated defect pairs have already shown annihilation to be heavily dependent on hydrodynamic interactions, which are beyond the XY model. Machine learning methods have recently been applied to analyze dense textures of defects in freely suspended smectic C films [1]. In this work, we apply these machine learning methods to analyze high-speed microscopy images of defect annihilation in quenched films. Due to the power-law scaling of defect annihilation, deviations from the XY model are predicted to be largest at early times, making this a highly sensitive test of the applicability of the XY model to quasi-2D smectic LC.