| 长时相干效应与分形布朗运动 |
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| 引用本文： | 王克钢,龙期威.长时相干效应与分形布朗运动[J].高压物理学报,1991,5(1):52-56. |
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| 作者姓名： | 王克钢 龙期威 |
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| 作者单位： | 中国科学院金属研究所
(王克钢)，中国科学院国际材料物理中心(龙期威) |
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| 摘 要： | 我们研究了阻尼布朗粒子，在具有幂律长时相干C(t)~t-β（0<β<1，1<β<2）的无规涨落力作用下的运动情况。我们发现它是作分形布朗运动，而不是作普通的布朗运动，而且，找出了分形布朗运动的有效Fokker-Planck方程，以及相应的精确解。于是第一次把长时相干效应和分形布朗运动建立了定量的联系。
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| 关 键 词： | 分形 布朗及分形布朗运动 扩散 Fokker-Planck方程 |
| 收稿时间： | 1990-07-20; |
LONG-TIME CORRELATION EFFECTS AND FRACTAL BROWNIAN MOTION |
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| Wang Kegang. Long Qiwei.LONG-TIME CORRELATION EFFECTS AND FRACTAL BROWNIAN MOTION[J].Chinese Journal of High Pressure Physics,1991,5(1):52-56. |
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| Authors: | Wang Kegang Long Qiwei |
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| Institution: | 1. Institute of Metal Research, Academia Sinica, Shenyang 110015, China;2. International Center for Materials Physics, Academia Sinica, Shenyang 110015, China |
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| Abstract: | We present a comprehensive study of the motion of a damped Brownian particle undergoing a randomly fluctuating force with zero mean and a correlation function of a power-law time dependence, or C(t)~t-β, 0<β<1, 1<β<2, instead of the Dirac delta-function. It is evident that this motion is fractional Brownian motion or fractal Brownian motion (fBm). The effective Fokker-Planck equation for fBm and its solution for fBm are presented. We have also established the quantitative relation of long-time correlation of power law time dependence to the fBm and anomalous diffusion. |
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| Keywords: | fractal Brownian and fractal Brownian motion diffusion Fokker-Planck equation |
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