The Vortex Kinetics of Conserved and Non-conserved O(n) Models

TL;DR

This paper develops an analytical approach to study vortex motion in conserved and non-conserved phase-ordering models, validated by numerical simulations, and introduces new measurements of vortex speed and position distributions.

Contribution

It provides a novel analytical method for vortex pair dynamics and first-time measurements of vortex distributions in conserved models, extending to scalar order parameters.

Findings

Analytical speed and position distribution functions match previous results in non-conserved models.

Numerical simulations confirm theoretical predictions for non-conserved vortices.

First measurements of vortex speed distribution in conserved models show large speed tail accuracy but small speed discrepancies.

Abstract

We study the motion of vortices in the conserved and non-conserved phase-ordering models. We give an analytical method for computing the speed and position distribution functions for pairs of annihilating point vortices based on heuristic scaling arguments. In the non-conserved case this method produces a speed distribution function consistent with previous analytic results. As two special examples, we simulate the conserved and non-conserved O(2) model in two dimensional space numerically. The numerical results for the non-conserved case are consistent with the theoretical predictions. The speed distribution of the vortices in the conserved case is measured for the first time. Our theory produces a distribution function with the correct large speed tail but does not accurately describe the numerical data at small speeds. The position distribution functions for both models are measured for the first time and we find good agreement with our analytic results. We are also able to extend this method to models with a scalar order parameter.