无限视界洛伦兹气体中粒子的色散
Dispersion of particles in an infinite-horizon Lorentz gas
摘要：
考虑具有无限视界的二维洛伦兹气体。该范式模型由点状粒子与排列在周期性晶格上的固定散射体进行弹性碰撞组成。严格地表明，当$t\to\infty$时，颗粒的分布是高斯分布。然而，收敛到这个极限是超低的，因此它实际上是无法达到的。本文给出了洛伦兹气体动力学在物理相关时间尺度上的解析解，并发现其远尾密度衰减符合普适的指数幂律$-3$。我们还表明，散射体的安排是印记的分布的形状。
英文摘要：
We consider a two-dimensional Lorentz gas with infinite horizon. This paradigmatic model consists of pointlike particles undergoing elastic collisions with fixed scatterers arranged on a periodic lattice. It was rigorously shown that when $t\to\infty$, the distribution of particles is Gaussian. However, the convergence to this limit is ultraslow, hence it is practically unattainable. Here we obtain an analytical solution for the Lorentz gas' kinetics on physically relevant timescales, and find that the density in its far tails decays as a universal power law of exponent $-3$. We also show that the arrangement of scatterers is imprinted in the shape of the distribution.
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