Fluctuations and Order

Abstract:

Normally, we would expect very large fluctuations to destroy order in a statistical state. However in a class of non-equilibrium statistical systems, a new type of state arises in which giant fluctuations coexist with long-range order. Such states arise in a number of systems and have interesting static and time-dependent properties. The approach to the ordered state is described by a singular scaling function, marking the breakdown of the Porod law. This has been observed in models of driven passive particles, as also in models of active biological systems and granular media, and in experiments on vibrated rods.

Interestingly, a single order parameter is insufficient, and we argue that a larger set is required to capture the essence of the phenomenon.