Creep dynamics of elastic manifolds via exact transition pathways

Alejandro B. Kolton 1, Alberto Rosso 2, Thierry Giamarchi 3, Werner Krauth 4

Physical Review B 79 (2009) 184207

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.

  • 1. Centro Atomico Bariloche,
    Centro Atómico Bariloche
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. DPMC (DPMC-MaNEP),
    University of Geneva
  • 4. Laboratoire de Physique Statistique de l'ENS (LPS),
    CNRS : UMR8550 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – Ecole Normale Supérieure de Paris - ENS Paris