Action minimization and macroscopic interface motion under forced displacement

TL;DR

This paper analyzes the optimal macroscopic interface motion in a one-dimensional non-local evolution model derived from a microscopic stochastic spin system, revealing different movement regimes based on displacement and time.

Contribution

It introduces a large deviations framework for interface motion in a non-local model and characterizes the optimal displacement strategies.

Findings

Interface moves at constant speed for small R/T ratios.

Nucleation of the other phase occurs for larger R/T ratios.

Different regimes of interface motion are identified.

Abstract

We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be quantified by obtaining the large deviations cost functional from the underlying stochastic process. For such a functional, derived in a companion paper, we investigate the optimal way for a macroscopic interface to move from an initial to a final position distant by R within fixed time T. We find that for small values of R/T the interface moves with a constant speed, while for larger values there appear nucleations of the other phase ahead of the front.