论文标题
洛伦兹镜模型在1D缸上的定位长度的多项式结合
Polynomial bound for the localization length of Lorentz mirror model on the 1D cylinder
论文作者
论文摘要
我们考虑Lorentz镜像模型和曼哈顿模型在均匀宽度气缸$ \ Mathbb {z} \ times（\ Mathbb {Z}/2N \ Mathbb {z}）= \ {（x，y）：x，y \ in \ in \ in \ mathbb {z}，1 \ leq y q y q y q y q y q y q y q y q y q y q y q y q y q y q yq yq yq yq yq yq yq yq y q yq y q y q y q}对于这两种模型，我们都表明，对于足够大的$ n $，具有高概率，从$ x = 0 $开始的任何光线轨迹都包含在区域$ | x | x | \ leq o（n^{10}）$中。
We consider the Lorentz mirror model and the Manhattan model on the even-width cylinder $\mathbb{Z} \times (\mathbb{Z}/2n\mathbb{Z}) =\{(x,y):x,y\in \mathbb{Z}, 1\leq y\leq 2n\}$. For both models, we show that for large enough $n$, with high probability, any trajectory of light starting from the section $x=0$ is contained in the region $|x|\leq O(n^{10})$.
