盒中两个硬盘的精确跳跃和碰撞时间
Exact hopping and collision times for two hard discs in a box
摘要：
我们研究了两个圆盘在一个矩形盒子中进行牛顿（“惯性”）动力学和弹性碰撞的分子动力学。利用到台球模型的映射和遍历理论的关键结果，我们获得了以下事件之间的平均时间的精确的解析表达式：粒子的水平或垂直交换;壁碰撞;和圆盘碰撞。为此，我们计算四维构型空间中的体积和横截面积。我们比较了Monte Carlo和分子动力学模拟的分析结果，具有良好的协议。
英文摘要：
We study the molecular dynamics of two discs undergoing Newtonian ("inertial") dynamics, with elastic collisions in a rectangular box. Using a mapping to a billiard model and a key result from ergodic theory, we obtain exact, analytical expressions for the mean times between the following events: hops, i.e.~horizontal or vertical interchanges of the particles; wall collisions; and disc collisions. To do so, we calculate volumes and cross-sectional areas in the four-dimensional configuration space. We compare the analytical results against Monte Carlo and molecular dynamics simulations, with excellent agreement.
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