Noise and Topology in Driven Systems - an Application to Interface Dynamics

Abstract

Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing the position of the interface and an internal degree of freedom). The noise accounts for thermal fluctuations of such systems. The models considered show a saddle-node bifurcation and have furthermore homoclinic orbits, i.e., orbits leaving an unstable fixed point and returning to it. Such systems display intermittent behavior. The presence of noise combined with the topology of the phase space leads to unexpected behavior as a function of the bifurcation parameter, i.e., of the driving force of the system. We explain this behavior using saddle point methods and considering global topological aspects of the problem. This then explains the non-monotonous force-velocity dependence of certain driven interfaces.

References in corpus (4)

• Creep and flow regimes of magnetic domain wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy
• Width distribution of contact lines on a disordered substrate
• Thermally-Assisted Current-Driven Domain Wall Motion
• Depinning of domain walls with an internal degree of freedom

Cited by in corpus (5)

• Statistics of Avalanches with Relaxation, and Barkhausen Noise: A Solvable Model
• Driven interfaces: from flow to creep through model reduction
• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
• Thermally rounded depinning of an elastic interface on a washboard potential
• Hysteretic depinning of a particle in a periodic potential: Phase diagram and criticality