Soliton-dynamical approach to a noisy Ginzburg-Landau model

TL;DR

This paper introduces a dynamical phase space approach to analyze non-equilibrium transitions in a noisy Ginzburg-Landau model, focusing on soliton-mediated nucleation and propagation, and validates the theoretical predictions with numerical results.

Contribution

It provides a novel phase space framework for understanding transition pathways involving solitons in noisy field models, linking theory with numerical optimization.

Findings

Good agreement with numerical optimization studies

Characterization of transition pathways via soliton dynamics

Evaluation of the Arrhenius factor in the model

Abstract

We present a dynamical description and analysis of non-equilibrium transitions in the noisy Ginzburg-Landau equation based on a canonical phase space formulation. The transition pathways are characterized by nucleation and subsequent propagation of domain walls or solitons. We also evaluate the Arrhenius factor in terms of an associated action and find good agreement with recent numerical optimization studies.