Energy relaxation in discrete nonlinear lattices

We numerically investigate energy relaxation in discrete nonlinear lattices in one and two spatial dimensions. We find that energy relaxation follows a stretched exponential law, and we study its dependence on the initial temperature. We attribute this behavior to hierarchies of discrete breathers that relax with different time constants, leading to a hierarchy of relaxation time scales in the system. Using heuristic arguments, we derive a nonlinear diffusion equation for the local energy density of the oscillators that results in similar relaxation dynamics.