1D phonon scattering by discrete breathers

At the zero amplitude limit, the scattering of 1D phonons by a spatially symmetric exact breather is equivalent to the linear scattering by a time-periodic potential. We first study situations with a single-channel scattering where the breather reemits phonons only at the frequency of the incoming wave omega. In that case, the incoming flux of energy is proven to be identical to the outgoing flux (elastic scattering). An extension of Levinson's theorem is proven and illustrated numerically on examples. The influence of internal modes of the breather on the scattering outcome is analysed. We next study situations with a multi-channel scattering where phonons are reemitted not only at the frequency of the incoming wave omega but also at another harmonic frequency omega + n omega(b). For such a scattering, it is proven that the reemitted outgoing flux of energy is necessarily larger than the energy flux of the incoming wave. As a result, the breather radiates energy with a flux proportional to the incoming flux. Its energy decays slowly and linearly over a very long period of time until it reaches another regime. This prediction is confirmed by a numerical simulation. (C) 1998 Elsevier Science B.V.