Coherence, Chaos, and Broken Symmetry in Classical, Many-Body Dynamical Systems

It is argued in the context of coupled quadratic maps that macroscopically chaotic states do not occur in many-body systems with local interactions and random initial conditions. Such systems can exhibit chaos, but only locally; their collective behavior is periodic or stationary. The phase diagram for the coupled-map system as a function of control parameter and noise is presented, and the universality classes of the phase transitions identified.