## Evidence for non-ergodicity in quiescent states of periodically sheared suspensions

By: Julian Schrenk

From: University of Cambridge

At: Faculdade de Ciências, Ed. C1, 1.3.14

[2015-11-26]

Periodically sheared suspensions of large (non-Brownian) particles undergo a transition from continued collision to "random organisation" in "quiescent states" (where no particles collide), depending on shear amplitude and packing fraction [1,2]. We present simulations of an equilibrium statistical-mechanics model that uniformly samples the space of quiescent states at fixed number of particles, volume fraction, and maximum shear amplitude [3]. In our simulations, we compute the structural properties of this model as a function of density. We compare the results of our simulations with the structural data obtained in the corresponding non-equilibrium model of CortÃ© et al. [2]. We find that the structural properties of the non-equilibrium model are very different from those of the equilibrium model, even though the two models have exactly the same set of accessible states. This observation shows that the dynamical protocol does not sample all quiescent states with equal probability. In particular, we find that, whilst quiescent states prepared in a non-equilibrium protocol can be hyperuniform (i.e. low-wave-vector density fluctuations vanish in the limit that the wave-vector goes to zero) [4,5,6], ergodic sampling never leads to hyperuniformity. In addition, we observe ordering phase transitions and a percolation transition in the equilibrium model that do not show up in the non-equilibrium model. Conversely, the quiescent-to-diffusive transition in the dynamical model does not correspond to a phase transition, nor a percolation transition, in the equilibrium model.

[1] Nature 438, 997 (2005)

[2] Nat. Phys. 4, 420 (2008)

[3] arXiv:1510.01280

[4] Phys. Rev. Lett. 114, 110602 (2015)

[5] Phys. Rev. Lett. 114, 148301 (2015)

[6] Phys. Rev. Lett. 115, 108301 (2015)

**Project**UIDB/00618/2020