Breather mobility and the PN potential: Brief review and recent progress

TL;DR

This paper reviews the Peierls-Nabarro potential's role in breather mobility in lattices, discusses recent progress in reducing the PN barrier, and explores new mobility scenarios in 2D Kagome lattices, active media, and quantum regimes.

Contribution

It introduces two novel mobility scenarios in 2D Kagome lattices and active media, and analyzes quantum effects on breather mobility using an extended Bose-Hubbard model.

Findings

Small PN barrier enables mobility in Kagome lattices.

Stable dissipative solitons can travel in active media.

Quantum fluctuations hinder classical mode mobility, but rapid modes remain mobile.

Abstract

The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile. Several ways to improve the mobility by reducing the PN-barrier have been proposed during the last decade, and the first part gives a brief review of such scenarios in 1D and 2D. We then proceed to discuss two recently discovered novel mobility scenarios. The first example is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility of highly localized modes in a small-power regime. The second example is a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping, where exponentially localized, travelling discrete dissipative solitons may exist as stable attractors. Finally, using the framework of an extended Bose-Hubbard model, we show that while quantum fluctuations destroy the mobility of slowly moving, strongly localized classical modes, coherent mobility of rapidly moving states survives even in a strongly quantum regime.