晶体结构中的正常扩散和带隙的高维台球模型
Normal diffusion in crystal structures and higher-dimensional billiard models with gaps
摘要：
我们表明，无论是理论上还是数值上，三维周期性洛伦兹气体-粒子云散射离开硬球的晶体阵列-通常表现出正常的扩散，即使有间隙，粒子可以通过它而不会碰撞，即，当系统的视界无限大时只要这些差距不是“太大”（按尺寸衡量），情况就是如此。一个简单的三维模型具有不同类型的扩散制度的模拟结果进行说明，然后扩展到高维台球模型，其中包括硬球流体。
英文摘要：
We show, both heuristically and numerically, that three-dimensional periodic Lorentz gases -- clouds of particles scattering off crystalline arrays of hard spheres -- often exhibit normal diffusion, even when there are gaps through which particles can travel without ever colliding, i.e., when the system has an infinite horizon. This is the case provided that these gaps are not "too big", as measured by their dimension. The results are illustrated with simulations of a simple three-dimensional model having different types of diffusive regime, and are then extended to higher-dimensional billiard models, which include hard-sphere fluids.
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