Acoustic breathers in two-dimensional lattices

Details Acoustic breathers in two-dimensional lattices Acoustic breathers in two-dimensional lattices

1997-09-04

arxiv.org/abs/cond-mat/9709048v1

PHYSICAL REVIEW LETTERS,v.79(#24),4838-4841 DEC 15,1997

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevLett.79.4838

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 $a\approx 1.85$.

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