Dynamic fluctuations of elastic lines in random environments

¹ Centro Atómico Bariloche - 8400 San Carlos de Bariloche, Río Negro, Argentina
² Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata Deán Funes 3350, 7600, Mar del Plata, Argentina
³ Physics Department, Boston University - 590 Commonwealth Av. Boston MA 02215, USA
⁴ Université Pierre et Marie Curie-Paris VI, LPTHE UMR 7589 4 Place Jussieu, 75252 Paris Cedex 05, France
⁵ Laboratoire de Physique Théorique de l'École Normale Supérieure 24 rue Lhomond, 75231 Paris Cedex 05, France

Received: 8 May 2006
Accepted: 29 September 2006

Abstract

We study the fluctuations of the two-time-dependent global roughness of finite-size elastic lines in a quenched random environment. We propose a scaling form for the roughness distribution function that accounts for the two-time, temperature, and size dependence. At high temperature and in the final stationary regime before saturation the fluctuations are as the ones of the Edwards-Wilkinson interface evolving from typical initial conditions. We analyze the variation of the scaling function within the aging regime and with the distance from saturation. We speculate on the relevance of our results to describe the fluctuations of other non-equilibrium systems such as models at criticality.