具有猝灭二分无序的驱动系统的解析可解模型
Analytically solvable model of a driven system with quenched dichotomous disorder
摘要：
本文研究了一维分段线性随机势场中过阻尼粒子的受驱动力学。这种空间上的淬火无序的设置然后在粒子上施加二分变化的随机力。我们推导出粒子位置的概率密度函数的路径积分表示，并将感兴趣的量转换为傅立叶积分的形式。在这样做时，概率密度的演化可以在有限时间内进行分析研究。它表明，概率密度包含一个$δ$ -奇异贡献和一个规则的部分。前一部分在短时间内起主导作用，后一部分在大的进化时间内统治行为。详细阐明了当时间趋于无穷大时，概率密度向极限高斯形式的缓慢逼近。
英文摘要：
We perform a time-dependent study of the driven dynamics of overdamped particles which are placed in a one-dimensional, piecewise linear random potential. This set-up of spatially quenched disorder then exerts a dichotomous varying random force on the particles. We derive the path integral representation of the resulting probability density function for the position of the particles and transform this quantity of interest into the form of a Fourier integral. In doing so, the evolution of the probability density can be investigated analytically for finite times. It is demonstrated that the probability density contains both a $δ$-singular contribution and a regular part. While the former part plays a dominant role at short times, the latter rules the behavior at large evolution times. The slow approach of the probability density to a limiting Gaussian form as time tends to infinity is elucidated in detail.
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