dorsal/arxiv
View SchemaDiscrete Breathers
| Authors | S. Flach, C. R. Willis |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9704004 |
| URL | https://arxiv.org/abs/patt-sol/9704004 |
| DOI | 10.1016/S0370-1573(97)00068-9 |
Abstract
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices - quantum breathers. Finally we will formulate a new conceptual aproach capable of predicting whether discrete breather exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.
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"abstract": "Nonlinear classical Hamiltonian lattices exhibit generic solutions in the\nform of discrete breathers. These solutions are time-periodic and (typically\nexponentially) localized in space. The lattices exhibit discrete translational\nsymmetry. Discrete breathers are not confined to certain lattice dimensions.\nNecessary ingredients for their occurence are the existence of upper bounds on\nthe phonon spectrum (of small fluctuations around the groundstate) of the\nsystem as well as the nonlinearity in the differential equations. We will\npresent existence proofs, formulate necessary existence conditions, and discuss\nstructural stability of discrete breathers. The following results will be also\ndiscussed: the creation of breathers through tangent bifurcation of band edge\nplane waves; dynamical stability; details of the spatial decay; numerical\nmethods of obtaining breathers; interaction of breathers with phonons and\nelectrons; movability; influence of the lattice dimension on discrete breather\nproperties; quantum lattices - quantum breathers. Finally we will formulate a\nnew conceptual aproach capable of predicting whether discrete breather exist\nfor a given system or not, without actually solving for the breather. We\ndiscuss potential applications in lattice dynamics of solids (especially\nmolecular crystals), selective bond excitations in large molecules, dynamical\nproperties of coupled arrays of Josephson junctions, and localization of\nelectromagnetic waves in photonic crystals with nonlinear response.",
"arxiv_id": "patt-sol/9704004",
"authors": [
"S. Flach",
"C. R. Willis"
],
"categories": [
"patt-sol",
"cond-mat",
"nlin.PS"
],
"doi": "10.1016/S0370-1573(97)00068-9",
"title": "Discrete Breathers",
"url": "https://arxiv.org/abs/patt-sol/9704004"
},
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