SCATTERING THEORY FOR LATTICE OPERATORS IN DIMENSION d ≥ 3
SCATTERING THEORY FOR LATTICE OPERATORS IN DIMENSION d ≥ 3
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DOI：
10.1142/s0129055x12500201
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发表时间：
2011-09
影响因子：
1.8
通讯作者：
J. Bellissard;H. Schulz-Baldes
中科院分区：
文献类型：
--
作者：
J. Bellissard;H. Schulz-Baldes
本文分析了受有限范围杂质扰动的周期性紧束缚哈密顿量的散射理论。经典的能量梯度流用于构造未扰动哈密顿量的共轭（或膨胀）算子。对于维度 d ≥ 3，波算子由膨胀算子、自由解析和扰动的显式公式给出。从这个公式中，可以读出散射和时间延迟算子。使用指数定理方法，证明了莱文森定理，该定理在存在嵌入特征值和阈值奇点的情况下也成立。
This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension d ≥ 3, the wave operator is given by an explicit formula in terms of this dilation operator, the free resolvent and the perturbation. From this formula, the scattering and time delay operators can be read off. Using the index theorem approach, a Levinson theorem is proved which also holds in the presence of embedded eigenvalues and threshold singularities.