Memory and universality in interface growth

TL;DR

This paper investigates the universal aging and memory properties of one-dimensional interface growth processes, revealing a universal two-time correlation form and ergodicity breaking, supported by experimental evidence in turbulent liquid crystals.

Contribution

It derives the universal form of two-time aging dynamics in interface growth and demonstrates ergodicity breaking, linking theory with experimental observations.

Findings

Universal two-time aging dynamics predicted

Experimental evidence in liquid crystals supports universality

Discovery of ergodicity breaking in growth processes

Abstract

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.