单交换子理论中的传播估计
Propagation estimates in the one-commutator theory
摘要：
在量子力学理论的抽象框架中，状态的传播可以用共轭算子$A$来理解。由于极限吸收原理（ETM），对于相对于$A$具有良好正则性的哈密顿量，一个强有力的估计长期以来一直是已知的。我们研究了$H$相对于$A$具有较小规律性的情况，特别是在尚未确定LAP和不存在奇异连续谱的情况下。我们表明，在这种情况下，$H$的谱测度是一个Rajchman措施，我们得到一些传播估计。一个估计是最小逃逸速度的应用，而另一个估计依赖于改进的版本的ESTA公式。基于几个例子，包括连续和离散薛定谔算子，似乎后者的传播估计是一个新的结果，多维哈密顿。
英文摘要：
In the abstract framework of Mourre theory, the propagation of states is understood in terms of a conjugate operator $A$. A powerful estimate has long been known for Hamiltonians having a good regularity with respect to $A$ thanks to the limiting absorption principle (LAP). We study the case where $H$ has less regularity with respect to $A$, specifically in a situation where the LAP and the absence of singularly continuous spectrum have not yet been established. We show that in this case the spectral measure of $H$ is a Rajchman measure and we derive some propagation estimates. One estimate is an application of minimal escape velocities, while the other estimate relies on an improved version of the RAGE formula. Based on several examples, including continuous and discrete Schrödinger operators, it appears that the latter propagation estimate is a new result for multi-dimensional Hamiltonians.
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