The Prandtl–Tomlinson model of friction with stochastic driving

Abstract

We consider the classical Prandtl–Tomlinson model of a particle moving on a corrugated potential, pulled by a spring. In the usual situation in which pulling acts at constant velocity , the model displays an average friction force σ that relates to (for small as , where is a critical friction force. The possible values of β are well known in terms of the analytical properties of the corrugated potential. We study here the situation in which the pulling has, in addition to the constant velocity term, a stochastic term of mechanical origin. We analytically show how this term modifies the force-velocity dependence close to the critical force, and give the value of β in terms of the analytical properties of the corrugation potential and the scaling properties of the stochastic driving, encoded in the value of its Hurst exponent.