Memory and Universality in Interface Growth

Jacopo De Nardis, Pierre Le Doussal, and Kazumasa A. Takeuchi
Phys. Rev. Lett. 118, 125701 – Published 21 March 2017
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Abstract

Recently, very robust universal properties have been shown to arise in one-dimensional growth processes with local stochastic rules, leading to the Kardar-Parisi-Zhang (KPZ) 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 and we show from first principles the breaking of ergodicity that the KPZ time evolution exhibits. We provide corroborating experimental observations on a turbulent liquid crystal system, as well as a numerical simulation of the Eden model, and we demonstrate the universality of our predictions. These results may give insight into memory effects in a broader class of far-from-equilibrium systems.

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  • Received 2 December 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.125701

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsNonlinear DynamicsPolymers & Soft Matter

Authors & Affiliations

Jacopo De Nardis1,*, Pierre Le Doussal2,†, and Kazumasa A. Takeuchi3,‡

  • 1Département de Physique, Ecole Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
  • 2CNRS-LPTENS, Ecole Normale Supérieure, PSL Research University, 24 rue Lhomond, 75005 Paris, France
  • 3Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

  • *jacopo.de.nardis@phys.ens.fr
  • ledou@lpt.ens.fr
  • kat@kaztake.org

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Issue

Vol. 118, Iss. 12 — 24 March 2017

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