Dynamical freezing of relaxation to thermal equilibrium.

Slow processes in statistical physics are typically ascribed to the presence of high free energy barriers which require the emergence of strong fluctuations for them to be overcome. Certain slow phenomena, however, can occur also from purely dynamical effects. An example is the slowing-down of relaxation to equipartition due to phase-space regions characterized by a nearly integrable dynamics. In this contribution we intend to discuss a peculiar dynamical mechanism leading to an extremely slow relaxation process in a spatially extended nonlinear lattice. This phenomenon occurs when discrete breathers, $i.e.$, intrinsic localized nonlinear excitations, appear in the system. We will analyze this mechanism and its implications in the Discrete Nonlinear Schroedinger Equation (DNLSE) and show that it is due to an adiabatic invariant which freezes the dynamics of high-energy breathers. We conjecture that the resulting exponentially slow relaxation is a key ingredient contributing to the non-ergodic behavior observed in the DNLSE.