### Abstract

We investigate the energy loss process produced by damping the boundary atoms of a chain of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit solution of the harmonic problem: even in such a simple system nontrivial features emerge from the interplay of the different decay rates of Fourier modes. In particular, a crossover from an exponential to an inverse-square-root law occurs on a timescale proportional to the system size N. A further crossover back to an exponential law is observed only at much longer times (of the order N^{3}). In the nonlinear chain, the relaxation process is initially equivalent to the harmonic case over a wide time span, as illustrated by simulations of the ß Fermi-Pasta-Ulam model. The distinctive feature is that the second crossover is not observed due to the spontaneous appearance of breathers, i.e. space-localized time-periodic solutions, that keep a finite residual energy in the lattice. We discuss the mechanism yielding such solutions and also explain why it crucially depends on the boundary conditions.

Original language | English |
---|---|

Pages (from-to) | 9803-9814 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 34 |

Issue number | 46 |

DOIs | |

Publication status | Published - 23 Nov 2001 |

## Fingerprint Dive into the research topics of 'Slow energy relaxation and localization in 1D lattices'. Together they form a unique fingerprint.

## Cite this

*Journal of Physics A: Mathematical and General*,

*34*(46), 9803-9814. https://doi.org/10.1088/0305-4470/34/46/304