LETTER On putative incommensurate states of a finite Frenkel-Kontorova chain

TL;DR

This paper offers a simplified explanation of the phases in a finite Frenkel-Kontorova chain, critiques existing theories on commensurate and incommensurate states, and challenges the existence of an Aubry-phase transition in finite chains.

Contribution

It introduces a new, simpler explanation for the phases of finite Frenkel-Kontorova chains and critiques the concept of Aubry-phase transition in such systems.

Findings

Proposes a simplified model for chain phases

Critiques the theory of commensurate/incommensurate states for finite chains

Rejects the existence of Aubry-phase transition in finite chains

Abstract

We propose a new but simpler explanation of the phases of a Frenkel-Kontorova chain of atoms, and we demonstrate it by examples. Combined with this, we present a criticism of the theory of so-called commensurate and incommensurate states, especially for finite chains. We reject the putative observation of an Aubry-phase transition in a finite chain.