Field theory of disordered systems -- Avalanches of an elastic interface in a random medium

Abstract

In this thesis I discuss analytical approaches to disordered systems using field theory. Disordered systems are characterized by a random energy landscape due to heterogeneities, which remains fixed on the time scales of the phenomena considered. I focus specifically on elastic interfaces in random media, such as pinned domain walls in ferromagnets containing defects, fluid contact lines on rough surfaces, etc. The goal is to understand static properties (e.g. the roughness) of such systems, and their dynamics in response to an external force. The interface moves in avalanches, triggered at random points in time, separated by long periods of quiescence. For magnetic domain walls, this phenomenon is known as Barkhausen noise. I first study the model of a particle in a Brownian random force landscape, applicable to high-dimensional interfaces. Its exact solution for a monotonous, but time-varying driving force is obtained. This allows computing the joint distribution of avalanche sizes and durations, and their spatial and temporal shape. I then generalize these results to a short-range correlated disorder. Using the functional renormalization group, I compute the universal distributions of avalanche sizes, durations, and their average shape as a function of time. The corrections with respect to the Brownian model become important in sufficiently low dimension (e.g. for a crack front in the fracture of a solid). I then discuss connections to the rough phase of Kardar-Parisi-Zhang nonlinear surface growth, and an application to the variable-range hopping model of electric conductance in a disordered insulator.

PhD thesis, 198 pages

References in corpus (32)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Growing interfaces uncover universal fluctuations behind scale invariance
• An exact solution for the KPZ equation with flat initial conditions
• Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
• Universal Properties of the Four-Body System with Large Scattering Length
• Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
• Onset of dendritic flux avalanches in superconducting films
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Gaussian Statistics of Fracture Surfaces
• Dynamics below the depinning threshold
• Creep dynamics of elastic manifolds via exact transition pathways
• Creep motion of an elastic string in a random potential
• Universal Properties of Two-Dimensional Boson Droplets
• Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study
• Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Optimal fluctuation approach to a directed polymer in a random medium
• Numerical study of the Kardar-Parisi-Zhang equation
• Energetics and structural properties of three-dimensional bosonic clusters near threshold
• The One-dimensional KPZ Equation and the Airy Process
• Universal and non-universal tails of distribution functions in the directed polymer and KPZ problems
• Fluctuations in fluid invasion into disordered media
• On the equivalence of Reggeon field theory in zero transverse dimensions and reaction-diffusion processes
• Thermal rounding exponent of the depinning transition of an elastic string in a random medium
• Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions
• Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together
• Thermal rounding of the depinning transition in ultrathin Pt/Co/Pt films
• Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality
• Universal non stationary dynamics at the depinning transition
• The universal high temperature regime of pinned elastic objects
• Eddy current damping of a moving domain wall: beyond the quasistatic approximation
• Joint free energy distribution in the random directed polymer problem

Cited by in corpus (8)

• Distribution of joint local and total size and of extension for avalanches in the Brownian force model
• The Spatial Shape of Avalanches
• Viscoelastic Interfaces Driven in Disordered Media and Applications to Friction
• Correlations between avalanches in the depinning dynamics of elastic interfaces
• Gaps between avalanches in 1D Random Field Ising Models
• Equivalence of mean-field avalanches and branching diffusions: From the Brownian force model to the super-Brownian motion
• Analytical Methods and Field Theory for Disordered Systems
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles