The subtle road to equilibrium - or not?*

The influence that deviations from equilibrium have on the ergodic equipartitioned dynamics of classical and quantum systems has been widely investigated in the recent years.
Classically, systems of many interacting bodies are typically chaotic, and their microcanonical dynamics ensures that time averages and phase space averages are identical, in agreement with the assumption of ergodicity.
In proximity to an integrable limit the properties of the network of nonintegrable action space perturbations help decide whether i) ergodization time scales stay on the order of the Lyapunov times, or whether ii) the system fragments into regular regions - formed by coherent localized excitations with anomalously large lifetimes - and chaotic parts. In this latter case, the ergodization time scales overgrows the Lyapunov times, and the system enters a dynamical glass (DG) phase at a finite distance to the integrable limit.
We use a set of observables which turn into conserved quantities in the integrable limit to quantify the properties of the DG phase.
A sectioning of a typical trajectory by equilibrium Poincare manifolds detects the coherent excitations, whose statistics signals the onset of the DG phase since they control the ergodization time scales of the systems.
We forecast that our studies may be successfully extended to quantum models, where the DG phase could consist into a prelude of the MBL phase.