Overall time evolution in phase-ordering kinetics

TL;DR

This paper investigates the time evolution in phase-ordering kinetics with conserved order parameters, revealing how different regimes depend on wave vector and quench parameters, using Bray-Humayun and Cahn-Hilliard-Cook models.

Contribution

It provides a detailed analysis of the overall time evolution in phase-ordering kinetics, highlighting the dependence on wave vector and quench parameters, and offers a simple explanation for complex crossover phenomena.

Findings

Identification of a generic pattern: early linear, intermediate mean field, late asymptotic regimes.

Regimes' durations depend on wave vector and quench parameters.

Complex crossover behavior can be explained by Bray-Humayun model solutions.

Abstract

The phenomenology from the time of the quench to the asymptotic behavior in the phase-ordering kinetics of a system with conserved order parameter is investigated in the Bray-Humayun model and in the Cahn-Hilliard-Cook model. From the comparison of the structure factor in the two models the generic pattern of the overall time evolution, based on the sequence ``early linear - intermediate mean field - late asymptotic regime'' is extracted. It is found that the time duration of each of these regimes is strongly dependent on the wave vector and on the parameters of the quench, such as the amplitude of the initial fluctuations and the final equilibrium temperature. The rich and complex crossover phenomenology arising as these parameters are varied can be accounted for in a simple way through the structure of the solution of the Bray-Humayun model.