Memory and universality in interface growth

Understanding possible universal properties for systems far from equilibrium is much less developed than for their equilibrium counterparts and poses a major challenge to present day statistical physics. The study of aging properties, and how the memory of the past is conserved by the time evolution in presence of noise is a crucial facet of the problem. Recently, very robust universal properties were shown to arise in one-dimensional growth processes with local stochastic rules,leading to the Kardar-Parisi-Zhang universality class. Yet it has remained essentially unknown how fluctuations in these systems correlate at different times. Here we derive quantitative predictions for the universal form of the two-time aging dynamics of growing interfaces, which, moreover, turns out to exhibit a surprising breaking of ergodicity. We provide corroborating experimental observations on a turbulent liquid crystal system, which demonstrates universality. This may give insight into memory effects in a broader class of far-from-equilibrium systems.
Comment: 6 pages + supplemental material (5 pages). 9 figures