Self-consistent theory of intrinsic localized modes: application to monatomic chain

TL;DR

This paper develops a self-consistent linearized theory for intrinsic localized modes in anharmonic lattices, validated by molecular dynamics in monatomic chains, offering a new analytical approach to ILMs.

Contribution

The paper introduces a novel linearized theoretical framework for ILMs in anharmonic lattices, enabling analytical calculations and validation against simulations.

Findings

Excellent agreement between theory and molecular dynamics results.

The theory effectively reduces nonlinear ILM problems to linear ones.

Application demonstrated on monatomic chains.

Abstract

A theory of intrinsic localized modes (ILMs) in anharmonic lattices is developed, which allows one to reduce the original nonlinear problem to a linear problem of small variations of the mode. This enables us to apply the Lifshitz method of the perturbed phonon dynamics for the calculations of ILMs. In order to check the theory, the ILMs in monatomic chain are considered. A comparison of the results with the corresponding molecular dynamics calculations shows an excellent agreement.