Vortex Velocities in the O(n) Symmetric TDGL Model

TL;DR

This paper derives an explicit formula for vortex velocities in the O(n) symmetric TDGL model and analyzes their distribution during phase ordering, revealing a velocity scaling with the inverse of the characteristic length scale.

Contribution

It provides a new explicit expression for vortex velocities and their distribution in the O(n) symmetric TDGL model during phase ordering.

Findings

Vortex velocity scales as L^{-1} in the scaling regime.

Derived the vortex velocity probability distribution.

Confirmed the velocity scaling with the characteristic length scale.

Abstract

An explicit expression for the vortex velocity field as a function of the order parameter field is derived for the case of point defects in the O(n) symmetric time-dependent Ginzburg-Landau model. This expression is used to find the vortex velocity probability distribution in the gaussian closure approximation in the case of phase ordering kinetics for a nonconserved order parameter. The velocity scales as $L^{-1}$ in scaling regime where $L\approx t^{1/2}$ and t is the time after the quench.