Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis

2008/03/22 by Serguei Naboko, Naboko, Serguei, Irina Pchelintseva +3
Computer Science · Mathematics · Physics and Astronomy · #39A11 #39A12 #47A25 #47B36 #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:39A11 #msc:39A12 #msc:47A25 #msc:47B36

paper · pdf · doi:10.48550/arxiv.0803.3288

27 pages, 2 figures

arxiv created 2008/03/22 · openalex publication_date 2008/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we develop a method for obtaining uniform asymptotics, with respect to the spectral parameter, of the generalized eigenvectors. Our technique can be applied to a wide range of Jacobi matrices.

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