Cooling nonlinear lattices toward localisation

Abstract

We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localised vibrations dramatically slows down dissipation and gives rise to quasi-stationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension (1D), strong enough on--site coupling may yield stretched--exponential relaxation which is reminiscent of glassy dynamics. We illustrate the mechanism generating localised structures and discuss the crucial role of the boundary conditions. For two--dimensional (2D) lattices, the existence of a gap in the breather spectrum causes the localisation process to become activated. A statistical analysis of the resulting quasi-stationary state through the distribution of breathers' energies yield information on their effective interactions.