非线性摩擦随机运动的路径积分方法
Path integral approach to random motion with nonlinear friction
摘要：
利用路径积分方法，我们导出了一个非线性奇异Langevin方程的解析解，该方程已由P. - G. de Gennes作为一个简单的唯象模型的粘滑运动的固体物体上的振动水平表面。我们表明，该模型的最佳（或最可能的）路径可以分为两类的路径，这对应于物理上的滑动或滑移运动，其中的对象以非零的速度移动的基础表面，和粘滑运动，其中的对象是坚持表面有限的时间。这两种基本运动构成了许多具有固/固摩擦的复杂系统行为的基础，并自然地出现在de Gennes模型的路径积分框架中。
英文摘要：
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.
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