Stepwise quantum decay of self-localized solitons

The two-phonon decay of self-localized soliton in a one-dimensional monatomic anharmonic lattice caused by cubic anharmonicity is considered. It is shown that the decay takes place with emission of phonon bursts. The average rate of emission of phonons is of the order of vibrational quantum per vibrational period. Characteristic time of the relaxation is determined by the quantum anharmonicity parameter; this time may vary from a few (quantum lattices, large anharmonicity) to thousands (ordinary lattices, small anharmonicity) of vibrational periods.Comment: 6 pages, 3 figure

Discrete Breathers

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.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm

Dynamic Structure Factor and Dielectric Function of Valence Electrons in Lithium Hydride: An Inelastic X‐Ray Scattering Study at Finite Momentum Transfer

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