Movability of Localized Excitations in Nonlinear Discrete Systems - a Separatrix Problem

TL;DR

This paper investigates how internal degrees of freedom influence the ability of localized excitations to move in nonlinear lattices, revealing that such internal structures generally prevent defining a Peierls-Nabarro potential for their motion.

Contribution

It establishes generic properties of a movability separatrix in high-dimensional phase space and proves that internal degrees of freedom hinder the definition of a Peierls-Nabarro potential.

Findings

Internal degrees of freedom prevent defining a Peierls-Nabarro potential.

Analytical and numerical verification in Fermi-Pasta-Ulam chains.

Movability separatrix properties characterized in high-dimensional phase space.

Abstract

We analyze the effect of internal degrees of freedom on the movability properties of localized excitations on defect-free nonlinear Hamiltonian lattices by means of properties of a local phase space which is at least of dimension six. We formulate generic properties of a movability separatrix in this local phase space. We prove that due to the presence of internal degrees of freedom of the localized excitation it is generically impossible to define a Peierls-Nabarro potential in order to describe the motion of the excitations through the lattice. The results are verified analytically and numerically for Fermi-Pasta-Ulam chains.