Incorporating memory effects in phase separation processes

T Koide,G Krein,Rudnei O Ramos

doi:10.1016/j.physletb.2006.03.035

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. Finite-time memory effects are seen to affect the dynamics of phase transition at short times and have 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. These effects are important in several systems characterized by fast processes, like non-equilibrium dynamics in the early universe and in relativistic heavy-ion collisions.

Highlights

The dynamics of phase transitions depends on whether the order parameter that characterizes the different phases of a system is a conserved quantity or not
Fast phase transitions are expected to have happened in the early universe and most certainly characterize the phase transitions expected to occur in the highly excited matter formed in relativistic heavy-ion collisions (RHIC)
In the early universe such situations may have happened when the typical microscopic time scales for relaxation, given by the inverse of the decay width associated with particle dynamics, is larger than the Hubble time

Summary

Introduction

The dynamics of phase transitions depends on whether the order parameter that characterizes the different phases of a system is a conserved quantity or not. In different fields of physics and chemistry the dynamics of a conserved order parameter has been described phenomenologically by the Cahn–Hilliard (CH) equation [1]

Results

Conclusion