Acoustic breathers in two-dimensional lattices

TL;DR

This paper investigates the existence and properties of breathers in two-dimensional lattices with acoustic phonons, demonstrating their persistence and strain field characteristics through numerical calculations on a 70x70 lattice.

Contribution

It extends breather solutions to 2D lattices with acoustic phonons and demonstrates their continuation with strain fields using a generalized Newton method.

Findings

Breathers persist in 2D lattices with acoustic phonons.

Strain fields around breathers decay approximately as 1/r^{1.85}.

Breather solutions can be continued with additional potential terms.

Abstract

The existence of breathers (time-periodic and spatially localized lattice vibrations) is well established for i) systems without acoustic phonon branches and ii) systems with acoustic phonons, but also with additional symmetries preventing the occurence of strains (dc terms) in the breather solution. The case of coexistence of strains and acoustic phonon branches is solved (for simple models) only for one-dimensional lattices. We calculate breather solutions for a two-dimensional lattice with one acoustic phonon branch. We start from the easy-to-handle case of a system with homogeneous (anharmonic) interaction potentials. We then easily continue the zero-strain breather solution into the model sector with additional quadratic and cubic potential terms with the help of a generalized Newton method. The lattice size is $70\times 70$. The breather continues to exist, but is dressed with a strain field. In contrast to the ac breather components, which decay exponentially in space, the strain field (which has dipole symmetry) should decay like $1/r^a, a=2$. On our rather small lattice we find an exponent $a\approx 1.85$.