Possibilities and Limitations of Gaussian Closure Approximations for Phase Ordering Dynamics

TL;DR

This paper critically examines Gaussian closure approximations in phase ordering dynamics, highlighting their limitations and demonstrating their fundamental flaws, especially in conserved order parameter cases.

Contribution

It clarifies the differences between Gaussian assumptions, analyzes their validity, and shows the breakdown of these approximations in certain phase ordering scenarios.

Findings

Different Gaussian approaches yield inconsistent results.

Gaussian assumption is fundamentally flawed for conserved order parameters.

Limitations of Gaussian closure are discussed in detail.

Abstract

The nonlinear equations describing phase ordering dynamics can be closed by assuming the existence of an underlying Gaussian stochastic field which is nonlinearly related to the observable order parameter field. We discuss the relation between different implementations of the Gaussian assumption and consider the limitations of this assumption for phase ordering dynamics. The fact that the different approaches gives different results is a sign of the breakdown of the Gaussian assumption. We concentrate on the non-conserved order parameter case but also touch on the conserved order parameter case. We demonstrate that the Gaussian assumption is fundamentally flawed in the latter case.