Domain wall propagation and nucleation in a metastable two-level system

TL;DR

This paper develops a dynamical framework for understanding non-equilibrium transitions in a noisy one-dimensional system, focusing on domain wall nucleation and propagation, with results aligning well with numerical studies.

Contribution

It introduces a canonical phase space approach to analyze domain wall dynamics in a stochastic Ginzburg-Landau model, providing analytical solutions and transition pathway characterization.

Findings

Derivation of nonlinear domain wall solutions with diffusive modes

Characterization of transition pathways via nucleation and propagation of domain walls

Quantitative agreement with numerical optimization results

Abstract

We present a dynamical description and analysis of non-equilibrium transitions in the noisy one-dimensional Ginzburg-Landau equation for an extensive system based on a weak noise canonical phase space formulation of the Freidlin-Wentzel or Martin-Siggia-Rose methods. We derive propagating nonlinear domain wall or soliton solutions of the resulting canonical field equations with superimposed diffusive modes. The transition pathways are characterized by the nucleations and subsequent propagation of domain walls. We discuss the general switching scenario in terms of a dilute gas of propagating domain walls and evaluate the Arrhenius factor in terms of the associated action. We find excellent agreement with recent numerical optimization studies.