MOTION OF A HEAVY PARTICLE IN AN INFINITE ONE DIMENSIONAL GAS OF HARD SPHERES
MOTION OF A HEAVY PARTICLE IN AN INFINITE ONE DIMENSIONAL GAS OF HARD SPHERES
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DOI：
10.1007/bf00536757
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发表时间：
1971-01-01
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影响因子：
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通讯作者：
HOLLEY, R
中科院分区：
文献类型：
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作者：
HOLLEY, R
在本文中，我们找到了一个大的重粒子与多个轻粒子碰撞运动的概率模型。具体情况如下。考虑一个一维世界，其中有无数个随机分布的粒子，每个粒子都独立于其他粒子运动，除了碰撞。在我们的模型中，粒子将以恒定的速度运动，直到它们与其他粒子碰撞。我们假设所有的碰撞都是完全弹性的，动量和能量守恒;因此，当两个质量相同的粒子碰撞时，它们只是交换速度。现在我们要讨论的问题是描述一个比其他粒子重得多的粒子的行为。在开始讨论这个问题之前，考虑一个如上所述的系统，在这个系统中，质量相等的粒子从所有偶数开始，每个粒子都独立地以概率89的速度1开始。我们将把从零开始的粒子视为一个特殊的粒子。很明显，如果我们在每个单位时间后观察这个粒子，它将执行简单的随机行走。然而，事实并非如此。如果我们用X（t）表示我们的特殊粒子在时间t的位置，下面的定理是正确的。(See比林斯利[1]第68页的证明。）
In this paper we find a probabilistic model for the motion of a large heavy particle colliding with many light particles. The physical situation is as follows. Consider a one dimensional world in which there are countably many particles distributed at random and each is moving independently of the others except for collisions. In our model the particles will move with constant velocity until they collide with other particles. We will assume that all collisions are perfectly elastic, conserving momentum and energy; and therefore, when two particles with the same mass collide, they simply exchange velocities. Now the problem that we will be concerned with is to describe the behavior of a particle which is much heavier than the others.Before beginning on this problem consider a system as described above in which particles of equal mass are started at all of the even integers and each is independently given a velocity ___ 1 with probability 89 We will consider the one which started at zero as a distinguished particle. It is clear that if we observe this particle after every unit time, it will be performing a simple random walk. However, more than this is true. If we denote by X (t) the position of our distinguished particle at time t, the following theorem is true.(See Billingsley [1] p. 68 for the proof.)