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We introduce and analyze a system of two coupled partial differentialequations with external noise. The equations are constructed to modeltransitions of monovalent metallic nanowires with non-axisymmetric intermediateor end states, but also have more general applicability. They provide a rareexample of a system for which an exact solution of nonuniform stationary statescan be found. We find a transition in activation behavior as the intervallength on which the fields are defined is varied. We discuss severalapplications to physical problems.

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