Contact processes in crowded environments

Abstract

Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions/contacts between particles in the steady state limit, while in the active phase collisions persist. To investigate this system at higher densities, we construct and study a conserved-particle-number contact process with novel three-body interactions, which are potentially more likely than two-body interactions at higher densities. For example, consider one active (diffusing) particle colliding with two inactive (non-diffusing) particles such that they become active, in addition to spontaneous inactivation. In mean-field, this system exhibits a continuous dynamical phase transition belonging to the conserved directed percolation universality class. Simulations on square lattices support the mean field result. In contrast, the three-body interaction requiring two active particles to activate one inactive particle exhibits a discontinuous transition. Finally, inspired by kinetically-constrained models of the glass transition, we investigate the "caging effect" at even higher particle densities to look for a second dynamical phase transition back to an inactive phase. Square lattice simulations suggest a continuous transition with a new set of exponents differing from conserved directed percolation, i.e. a new universality class for contact processes with conserved particle number.