Velocity autocorrelation of a free particle driven by a Mittag-Leffler noise: fractional dynamics and temporal behaviors.
Velocity autocorrelation of a free particle driven by a Mittag-Leffler noise: fractional dynamics and temporal behaviors.
复制标题
DOI：
10.1103/physreve.90.062103
复制
发表时间：
2014-12
期刊：
影响因子：
--
通讯作者：
A. Viñales;G. Paissan
中科院分区：
文献类型：
--
作者：
A. Viñales;G. Paissan
研究了受Mittag-Leffler噪声驱动的自由粒子广义朗之万方程的动力学相图，给出了表征不同动力学区域的Mittag-Leffler函数的临界曲线和指数参数的临界值。考虑到Mittag-Leffer记忆核的建模对应于幂二阶记忆核，我们证明了速度自相关函数(VACF)的广义朗之万方程可以转化为分数朗之万方程。在超扩散情况下，我们的结果显示了VACF的振荡和负关联，这是通常的幂定律噪声模型所不能提供的。
We investigate the dynamical phase diagram of the generalized Langevin equation of the free particle driven by a Mittag-Leffler noise and show critical curves and a critical value of the exponent parameter of the Mittag-Leffler function that mark different dynamical regimes. By considering that the modeling of a Mittag-Leffer memory kernel corresponds to a power-law second-order memory kernel, we show that the generalized Langevin equation of the velocity autocorrelation function (VACF) is transformed in a fractional Langevin equation. In the superdiffusive case our results exhibit oscillations and negative correlations of the VACF that are not provided by the usual power-law noise model.