无限视界台球：高斯和列维普适性类之间的边界处的输运
Infinite horizon billiards: Transport at the border between Gauss and Lévy universality classes
摘要：
我们考虑在两个台球模型，无限的地平线洛伦兹气体和体育场通道的运输，粒子的传播包的分析结果。我们首先得到碰撞之间的旅行时间的累积分布函数，它表现出非解析行为。利用更新假设和Lévy walk模型，我们得到了粒子的概率密度。对于洛仑兹气体，它与已知的高斯传播子相比显示出显著的差异，因为后者仅在极长时间内有效。特别是，我们展示了沿着无限走廊扩散的粒子羽流，创造了密度的幂律尾部。我们证明了缓慢的收敛速度通过求和的独立同分布的随机变量之间的边界Lévy和高斯定律。更新假设适用于具有中等大小散射中心的洛伦兹气体，但由于强的时间相关性，在体育场通道中失败。我们的分析结果支持数值采样。
英文摘要：
We consider transport in two billiard models, the infinite horizon Lorentz gas and the stadium channel, presenting analytical results for the spreading packet of particles. We first obtain the cumulative distribution function of traveling times between collisions, which exhibits non-analytical behavior. Using a renewal assumption and the Lévy walk model, we obtain the particles' probability density. For the Lorentz gas, it shows a distinguished difference when compared with the known Gaussian propagator, as the latter is valid only for extremely long times. In particular, we show plumes of particles spreading along the infinite corridors, creating power-law tails of the density. We demonstrate the slow convergence rate via summation of independent identically distributed random variables on the border between Lévy and Gauss laws. The renewal assumption works well for the Lorentz gas with intermediately sized scattering centers, but fails for the stadium channel due to strong temporal correlations. Our analytical results are supported with numerical samplings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
