Universality in relaxation dynamics of systems near integrability

We study the long-time relaxation dynamics of many-body systems by examining the spectral functions of the autocorrelations. We explore several models near integrability by introducing small integrability breaking perturbations. Similar to critical behavior near continuous phase transitions, we find that the systems are characterized by extremely slow relaxation dynamics close to integrability and exhibit universal finite time scaling behavior. Our results suggest that integrable regimes bear close similarities to critical points.