Velocity Distribution for Strings in Phase Ordering Kinetics

TL;DR

This paper derives an explicit velocity distribution for string defects in phase-ordering kinetics using the Ginzburg-Landau model, revealing scaling laws and defect annihilation behaviors over time.

Contribution

It provides a novel explicit expression for string velocity fields and their probability distribution in phase-ordering dynamics for the first time.

Findings

Velocity scales as t^{-1/2} at long times.

Velocity distribution has a tail decaying as V^{-(2d+2-n)}.

Results apply to both point and string defects in d dimensions.

Abstract

The continuity equations expressing conservation of string defect charge can be used to find an explicit expression for the string velocity field in terms of the order parameter in the case of an O(n) symmetric time-dependent Ginzburg-Landau model. This expression for the velocity is used to find the string velocity probability distribution in the case of phase-ordering kinetics for a nonconserved order parameter. For long times $t$ after the quench, velocities scale as $t^{-1/2}$. There is a large velocity tail in the distribution corresponding to annihilation of defects which goes as $V^{-(2d+2-n)}$ for both point and string defects in $d$ spatial dimensions.