We provide evidence of an extremely slow thermalization occurring in the discrete nonlinear Schrödinger model. At variance with many similar processes encountered in statistical mechanics - typically ascribed to the presence of (free) energy barriers - here the slowness has a purely dynamical origin: it is due to the presence of an adiabatic invariant, which freezes the dynamics of a tall breather. Consequently, relaxation proceeds via rare events, where energy is suddenly released towards the background. We conjecture that this exponentially slow relaxation is a key ingredient contributing to the nonergodic behavior recently observed in the negative-temperature region of the discrete nonlinear Schrödinger equation.
Iubini, S., Chirondojan, L., Oppo, G. L., Politi, A., & Politi, P. (2019). Dynamical Freezing of Relaxation to Equilibrium. Physical Review Letters, 122(8). https://doi.org/10.1103/PhysRevLett.122.084102