脉冲噪声驱动的分数阶调和振子的均方位移
Mean square displacements of fractional harmonic oscillators driven by an impulsive noise

利用光钳实验获取浸没于粘弹性介质中粒子的均方位移数据并为其建模是微观流变学中计算介质的局部响应函数的一种常用方法. 本文研究一类由单个脉冲噪声驱动的分数阶调和振子的均方位移. 利用Laplace变换及双Laplace变换技巧，本文得到了振子位移的均值、方差及双时相关函数，进而求得均方位移的解析表达式. 基于Mittag-Leffler函数的渐进性质，本文研究了振子在短时和长时情形下的不同扩散行为. 研究表明，在短时振子弹道扩散而在长时则幂律地趋近于一个均衡值，即被板扎.
Mean square displacement have been extensively used to evaluate the response function of viscoelastic medium in laser tweezer experiments. In this paper, by using the Laplace and double Laplace transform techniques, we obtain exact solution of the fractional harmonic oscillator driven by an impulsive noise. Then, the mean, variance, two-time correlation function and mean square displacement are given in terms of the time-lag. Furthermore, diffusive behavior of the oscillator is investigated by considering asymptotic behavior of the mean square displacement. It is showed that the oscillator undergoes a ballistic motion for short time-lag and a power-law decay to a equilibrium point for long time-lag