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

TL;DR

This paper investigates how noise and phase space topology influence bifurcation and intermittent behavior in driven interface systems, explaining non-monotonous force-velocity relationships through saddle point analysis.

Contribution

It introduces a generalized model with a 2D phase space for interface dynamics, revealing complex bifurcation and topological effects on system behavior under noise.

Findings

Identification of saddle-node bifurcations in the model

Demonstration of homoclinic orbits causing intermittency

Explanation of non-monotonous force-velocity dependence

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.