Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise
Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise
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DOI：
10.1063/1.4863478
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发表时间：
2014-02
影响因子：
1.3
通讯作者：
Trifce Sandev;R. Metzler;Ž. Tomovski
中科院分区：
文献类型：
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作者：
Trifce Sandev;R. Metzler;Ž. Tomovski
我们研究了存在调和势的广义分数阶朗之万方程。推导了平均速度和质点位移、均方位移、位置和速度相关函数以及归一化位移相关函数的一般表达式。我们报道了内摩擦和外摩擦情况下的精确结果，即当驱动噪声是内部的，从而满足涨落-耗散关系时，或者当噪声是外部的时候。研究了广义随机振子的渐近行为，并考虑了高粘性阻尼(过阻尼限)的情况。观察到与规则阻尼谐振子不同的归一化位移关联函数的附加行为。此外，还得到了恒定外力情况和无外力情况。讨论了广义爱因斯坦关系对这一过程的有效性。所考虑的分数阶广义朗之万方程可用于模拟包括单文件扩散在内的异常扩散过程。
We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.