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

Propagation effects in superfluorescence

The evolution of a superfluorescent pulse is studied in the region of large sample lengths. A solution to the Maxwell-Bloch semiclassical equations is found by using the inverse scattering method. It has the form of a one-soliton solution with varying parameters. Dependence on the pulse width and the retarded time is found without further approximations. These parameters are shown to be independent of the inhomogeneous broadening time. Their values are in good agreement with experiment. Asymmetry of the pulse is also investigated