Dynamic Statistical Scaling in the Landau-de Gennes Theory of Nematic Liquid Crystals

TL;DR

This paper studies the long-term behavior of correlation functions in nematic liquid crystals during phase transition, confirming a self-similar scaling hypothesis within the Landau-de Gennes theoretical framework.

Contribution

It provides the first rigorous confirmation of the self-similar asymptotic behavior of correlation functions in nematic liquid crystals during phase transition.

Findings

Confirmed the self-similar asymptotic behavior of the correlation function

Analyzed possible alternative scaling behaviors

Validated theoretical predictions with mathematical analysis

Abstract

We investigate the asymptotic behaviour of a correlation function associated with a nematic liquid crystal system undergoing an isotropic-nematic phase transition following an instantaneous change of temperature. Within the setting of Landau-de Gennes theory, we confirm a hypothesis in the condensed matter physics literature on the average self-similar behaviour of the correlation function in the asymptotic regime at time infinity. In the final sections, we comment on other possible scaling behaviour of the correlation function.