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

摘要

Motivated by a stochastic differential equation describing the dynamics ofinterfaces, we study the bifurcation behavior of a more general class of suchequations. 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 modelsconsidered show a saddle-node bifurcation and have furthermore homoclinicorbits, i.e., orbits leaving an unstable fixed point and returning to it. Suchsystems display intermittent behavior. The presence of noise combined with thetopology of the phase space leads to unexpected behavior as a function of thebifurcation parameter, i.e., of the driving force of the system. We explainthis behavior using saddle point methods and considering global topologicalaspects of the problem. This then explains the non-monotonous force-velocitydependence of certain driven interfaces.