论文标题
Schrödinger操作员的散射，其电势集中在子空间附近
Scattering for Schrödinger operators with potentials concentrated near a subspace
论文作者
论文摘要
我们研究了Schrödinger运营商的散射特性，其有限电位集中在$ \ Mathbb {r}^d $的子空间附近。对于此类操作员，我们表明了散射状态的存在，并将其正交补体描述为一组表面状态，这些状态由局限于子空间（例如纯点状态）的状态组成，并说出以适当的意义以sublinear速度逃脱它的状态。我们为不同系统提供表面状态的示例，包括沿子空间传播的系统以及任意缓慢逃脱子空间的系统。我们的证明使用对ENSS方法的新解释，以获得散射状态正交补体的动态表征。
We study the scattering properties of Schrödinger operators with bounded potentials concentrated near a subspace of $\mathbb{R}^d$. For such operators, we show the existence of scattering states and characterize their orthogonal complement as a set of surface states, which consists of states that are confined to the subspace (such as pure point states) and states that escape it at a sublinear rate, in a suitable sense. We provide examples of surface states for different systems including those that propagate along the subspace and those that escape the subspace arbitrarily slowly. Our proof uses a novel interpretation of the Enss method in order to obtain a dynamical characterisation of the orthogonal complement of the scattering states.
