Fluctuations of topological disclination lines in nematics: renormalization of the string model

TL;DR

This paper analyzes the fluctuation modes of nematic topological disclination lines, providing exact relaxation rates and showing that simple models underestimate fluctuation amplitudes, with implications for universal defect systems.

Contribution

It offers a complete solution to the fluctuation eigenmode problem for nematic disclination lines using the full tensor order parameter, refining the understanding of line tension and fluctuation amplitudes.

Findings

Exact relaxation rates and thermal fluctuation amplitudes are determined.

Simple string models underestimate fluctuation amplitudes due to neglect of higher modes.

The results have implications for universality in systems with line defects.

Abstract

The fluctuation eigenmode problem of the nematic topological disclination line with strength $\pm 1/2$ is solved for the complete nematic tensor order parameter. The line tension concept of a defect line is assessed, the line tension is properly defined. Exact relaxation rates and thermal amplitudes of the fluctuations are determined. It is shown that within the simple string model of the defect line the amplitude of its thermal fluctuations is significantly underestimated due to the neglect of higher radial modes. The extent of universality of the results concerning other systems possessing line defects is discussed.