Memory Effect and Fast Spinodal Decomposition

TL;DR

This paper investigates how incorporating a memory effect into the Cahn-Hilliard equation influences spinodal decomposition, revealing that memory delays the rapid growth of the order parameter and ensures finite propagation speed during phase transitions.

Contribution

It introduces a modified Cahn-Hilliard model with memory effects and analyzes its impact on the dynamics and causality of fast spinodal decomposition.

Findings

Memory effect delays the rapid growth of the order parameter.

Memory ensures finite group velocity, satisfying causality.

Short-time dynamics of phase transition are significantly affected.

Abstract

We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved order parameter. The introduced memory effect plays an important role to obtain a finite group velocity. Then, we discuss the constraint for the parameters to satisfy causality. The memory effect is seen to affect the dynamics of phase transition at short times and has the effect of delaying, in a significant way, the process of rapid growth of the order parameter that follows a quench into the spinodal region.