The Escape Problem in a Classical Field Theory With Two Coupled Fields

TL;DR

This paper models nanowire transitions using coupled PDEs with noise, providing exact solutions for nonuniform states and revealing a transition in activation behavior as system size varies.

Contribution

It introduces a novel coupled PDE system with exact solutions for nonuniform states, applicable to nanowire transition modeling and other physical systems.

Findings

Exact solutions for nonuniform stationary states

Identification of a transition in activation behavior

Applicability to physical problems involving nanowires

Abstract

We introduce and analyze a system of two coupled partial differential equations with external noise. The equations are constructed to model transitions of monovalent metallic nanowires with non-axisymmetric intermediate or end states, but also have more general applicability. They provide a rare example of a system for which an exact solution of nonuniform stationary states can be found. We find a transition in activation behavior as the interval length on which the fields are defined is varied. We discuss several applications to physical problems.