论文标题
定期和随机媒体中的弹道运输
Ballistic transport in periodic and random media
论文作者
论文摘要
我们证明了所有订单的弹道传输，即$ \ lvert x^m \ mathrm {e}^{ - \ mathrm {i} th}ψ\ rvert \ asymp t^m $，用于以下模型：$ \ mathbb {z}^d $，$，$ {z}^d $，lap $，lap lap lap lap lap laplace on laplace on lapectiment： $ \ Mathbb {r}^d $上的Schrödinger运算符，以及定期图表上离散的定期Schrödinger操作员。在所有情况下，我们将$ \ lvert x^m \ mathrm {e}^{ - \ mathrm {i} th}ψ\ rvert/t^m $的限制的确切表示为$ t \ to+\ infty $。然后，我们转到有限图的通用覆盖物（它们是无限树），并在自然抬起电势时，证明了弹道传输，给出了定期模型，并且在树上具有随机的I.I.D. \电位时，给出了Anderson模型。然后讨论限制分布，以丰富运输理论。附录中详细介绍了一些一般的上限。
We prove ballistic transport of all orders, that is, $\lVert x^m\mathrm{e}^{-\mathrm{i}tH}ψ\rVert\asymp t^m$, for the following models: the adjacency matrix on $\mathbb{Z}^d$, the Laplace operator on $\mathbb{R}^d$, periodic Schrödinger operators on $\mathbb{R}^d$, and discrete periodic Schrödinger operators on periodic graphs. In all cases we give the exact expression of the limit of $\lVert x^m\mathrm{e}^{-\mathrm{i}tH}ψ\rVert/t^m$ as $t\to+\infty$. We then move to universal covers of finite graphs (these are infinite trees) and prove ballistic transport in mean when the potential is lifted naturally, giving a periodic model, and when the tree is endowed with random i.i.d.\ potential, giving an Anderson model. The limiting distributions are then discussed, enriching the transport theory. Some general upper bounds are detailed in the appendix.
