Title: Universal force-force correlations for driven, disordered elastic interfaces: What we can learn from them. Speaker: Cathelijne ter Burg

Abstract:

Elastic interfaces driven in a disordered medium exhibit a phenomenon called avalanches: periods of rapid movement in between states where the interface is pinned. Today it is understood that the minimal ingredients to describe these systems are an elastic energy competing with the disorder energy, and a confining potential. When the center $w $ of this confining potential is slowly increased, one reaches the zero-temperature depinning transition, where physics becomes universal. One can measure correlations of the interface’s center-of-mass position as a function of w, which depends on the driving velocity. Its zero-velocity limit, $\Delta(w)$, is the principle observable in the field-theory approach to disordered systems. In this talk, I will discuss what can be learned from this observable by measuring it in simulations and experiment. After an introduction to the theory of disordered systems and the field theory, I present a collection of results obtained during my PhD:

I will present measurements of $\Delta(w) $in soft ferro-magnets. It allows us to distinguish between magnets with short-range and long-range elasticity. The latter class is a system at its critical dimension, and is in the literature incorrectly described by mean field theory, equated to the ABBM model. The ABBM model replaces the system by a single degree of freedom, the domain wall’s center of mass, with the disorder modelled as a random walk. As a consequence, $\Delta(0) - \Delta(w)$ grows unboundedly. These new measurements show that instead the physical $\Delta (w) $is described by the one-loop FRG fixed point, invalidating mean field theory at the critical dimension. A bound is obtained which gives information about the degree of correlation in one’s sample. On the theoretical side I discuss a particle model, itself a mean field model, which described the crossover from ABBM to another mean field model called the discretised particle model, where forces are represented by needles at integer sites. This crossover can be studied numerically by simulating forces as an Ornstein-Uhlenbeck process.

I then discuss the effect of additional thermal fluctuations which allow the system to equilibrate. Questions one may ask are: How does the crossover from depinning to equilibrium take place? How do additional temperature fluctuations perturb the depinning fixed point, and how do velocity perturbations perturb the equilibrium fixed point. These questions are relevant for experiments on DNA-hairpin unzipping. Measuring $\Delta(w) $we can establish this experiment is in equilibrium and falls in the universality class of the Sinai model.