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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-（01，12）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
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-, 01, 12, 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.-
Key words:
- fractal /
- Brownian and fractal Brownian motion /
- diffusion /
- Fokker-Planck equation
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