Critical diffusivity in the reversibility-irreversibility transition of amorphous solids under oscillatory shear

Recently it was shown that under oscillatory shear at zero temperature an amorphous solid transitions from asymptotically periodic to asymptotically diffusive steady-state at a critical maximal strain amplitude. Current understanding of the physics behind this transition is lacking. Here we show, using computer simulations, evidence that the diffusivity of the vector of coordinates of the particles comprising an amorphous solid, when subject to oscillatory shear, undergoes a second order phase transition at the reversibility-irreversibility transition point. We explain how such a transition is consistent with dissipative forced dynamics on a complex energy landscape, such as is known to exist in amorphous solids. We demonstrate that as the forcing increases, more and more state-space volume becomes accessible to the system, making it less probable for the state-space trajectory of the system to self-intersect and form a limit-cycle, which explains the slowing-down observed at the transition.