Absolutely continuous and pure point spectra of discrete operators with sparse potentials

2021/10/17 by S. Molchanov, Molchanov, S., O. Safronov +3
Mathematics · #39A14 #47A10 #81Q10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2110.08684

openalex publication_date 2021/10/17 · openalex created_date 2022/11/07 · openalex updated_date 2026/07/28

Abstract

We consider the discrete Schrödinger operator H=-Δ+V with a sparse potential V and find conditions guaranteeing either existence of wave operators for the pair H and H₀=-Δ, or presence of dense purely point spectrum of the operator H on some interval [λ₀,0] with λ₀<0.

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