Band edge limit of the scattering matrix for quasi-one-dimensional discrete Schrödinger operators

2020/08/05 by Miguel Ballesteros, Gerardo Franco Córdova, Ballesteros, Miguel +5 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2008.02177

openalex publication_date 2020/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is about the scattering theory for one-dimensional matrix Schrödinger operators with a matrix potential having a finite first moment. The transmission coefficients are analytically continued and extended to the band edges. An explicit expression is given for these extensions. The limits of the reflection coefficients at the band edges is also calculated.

Cited by

• Factorization for the matrix-valued general Jacobi system on the full-line lattice
• Topological Levinson's theorem and corrections at thresholds: the full picture in a quasi-1D example

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