Scattering theory for lattice operators in dimension d ≥ 3

Bellissard J, Schulz-Baldes H (2012)


Publication Type: Journal article, Original article

Publication year: 2012

Journal

Publisher: World Scientific Publishing

Book Volume: 24

Pages Range: 1250020-1250071

URI: http://de.arxiv.org/abs/1109.5459

DOI: 10.1142/S0129055X12500201

Abstract

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.

 

 

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APA:

Bellissard, J., & Schulz-Baldes, H. (2012). Scattering theory for lattice operators in dimension d ≥ 3. Reviews in Mathematical Physics, 24, 1250020-1250071. https://dx.doi.org/10.1142/S0129055X12500201

MLA:

Bellissard, Jean, and Hermann Schulz-Baldes. "Scattering theory for lattice operators in dimension d ≥ 3." Reviews in Mathematical Physics 24 (2012): 1250020-1250071.

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