Vortex Velocity Pair Correlations

TL;DR

This paper analyzes the velocity correlations between vortex pairs during phase-ordering kinetics in systems with point defects, providing explicit formulas for their relative velocities influenced by other vortices and fluctuations.

Contribution

It introduces a detailed analysis of vortex velocity pair correlations in the n-vector model with time-dependent Ginzburg-Landau dynamics, including explicit velocity-distance relationships.

Findings

Most probable vortex-antivortex pairs have relative velocities inversely proportional to their separation.

Explicit coefficient for the velocity-distance relationship is derived.

The model accounts for effects of other vortices and order parameter fluctuations.

Abstract

The vortex velocity probability distribution for two distinct vortices is determined for the case of phase-ordering kinetics in systems with point defects. The n-vector model driven by time-dependent Ginzburg-Landau dynamics for a nonconserved order parameter is considered. The description includes the effects of other vortices and order parameter fluctuations. At short distances the most probable configuration is that a vortex-antivortex pair have only a nonzero relative velocity which is inversely proportional to the distance between them. The coefficient of proportionality is determined explicitly.