应用于量子系统的复对称算子的范数估计
Norm estimates of complex symmetric operators applied to quantum systems
摘要：
本文介绍了复对称算子理论的最新结果，并通过两个非平凡的例子说明了它们在薛定谔算子研究中的潜在用途。特别是，我们提出了一个公式计算的范数的一个紧凑的复对称算子。这一观察结果被应用于两个与量子力学系统相关的具体问题。首先，我们给出了具有谱隙的薛定谔算子的预解式和单粒子密度矩阵的指数衰减的精确估计。其次，我们提供了新的方法来评估薛定谔算子出现在复杂的标度理论的共振预解范数。
英文摘要：
This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schrödinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schrödinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schrödinger operators appearing in the complex scaling theory of resonances.
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