外场中洛伦兹气体高速无规飞行过程的自由程
The free path in a high velocity random flight process associated to a Lorentz gas in an external field
摘要：
研究了外场作用下变密度随机飞行模型自由程随粒子初速度趋于无穷大的渐近行为。随机飞行模型，我们研究自然出现的玻尔兹曼-格拉德极限的随机洛伦兹气体在外场的存在下。通过分析自由程的持续时间，我们得到了自由程的渐近均值和方差关于外场和散射体密度的精确形式。因此，我们得到一个扩散近似的联合过程中观察到的粒子在反射时间和在自由飞行中花费的时间量。
英文摘要：
We investigate the asymptotic behavior of the free path of a variable density random flight model in an external field as the initial velocity of the particle goes to infinity. The random flight models we study arise naturally as the Boltzmann-Grad limit of a random Lorentz gas in the presence of an external field. By analyzing the time duration of the free path, we obtain exact forms for the asymptotic mean and variance of the free path in terms of the external field and the density of scatterers. As a consequence, we obtain a diffusion approximation for the joint process of the particle observed at reflection times and the amount of time spent in free flight.
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