A path integral approach to random motion with nonlinear friction

作者：Baule A^*; Cohen E G D; Touchette H

来源：Journal of Physics A-Mathematical and Theoretical, 2010, 43(2): 025003.

DOI：10.1088/1751-8113/43/2/025003

Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P-G de Gennes as a simple phenomenological model for the stick-slip motion of a solid object on a vibrating horizontal surface. We show that the optimal (or most probable) paths of this model can be divided into two classes of paths, which correspond physically to a sliding or slip motion, where the object moves with a non-zero velocity over the underlying surface, and a stick-slip motion, where the object is stuck to the surface for a finite time. These two kinds of basic motions underlie the behavior of many more complicated systems with solid/solid friction and appear naturally in de Gennes' model in the path-integral framework.

• 出版日期2010-1-15