Velocity Distribution of Topological Defects in Phase-Ordering Systems

TL;DR

This paper investigates the velocity distribution of topological defects in phase-ordering systems, deriving a power-law tail and providing approximate calculations for both conserved and nonconserved dynamics.

Contribution

It introduces a heuristic scaling framework for defect velocity distributions and extends the analysis to vector order parameters.

Findings

Power-law tail in velocity distribution with exponent p

Explicit relation p = 2+d/(z-1) for different dynamics

Approximate calculations using a gaussian closure scheme

Abstract

The distribution of interface (domain-wall) velocities ${\bf v}$ in a phase-ordering system is considered. Heuristic scaling arguments based on the disappearance of small domains lead to a power-law tail, $P_v(v) \sim v^{-p}$ for large v, in the distribution of $v \equiv |{\bf v}|$. The exponent p is given by $p = 2+d/(z-1)$, where d is the space dimension and 1/z is the growth exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to systems described by a vector order parameter.