Threshold phenomenon for a family of the Generalized Generalized Friedrichs models with the perturbation of rank one

2014/11/28 by Saidakhmat N. Lakaev, S. N. Lakaev, Maslina Darus +4
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Forms (bilinear #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.DS #math.FA #math.MP #math.SP #msc:47A10 #multilinear) 47A10 Spectrum #resolvent #sesquilinear

paper · pdf · doi:10.48550/arxiv.1412.0598

11 pages

arxiv created 2014/11/28 · openalex publication_date 2014/11/28 · arxiv updated 2014/12/02 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

A family H_μ(p), μ>0, p∈\T³ of the Generalized Firedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the three dimensional lattice \mathbb\Z³, is considered. The existence or absence of the unique eigenvalue of the operator H_μ(p) lying outside the essential spectrum, depending on the values of μ>0 and p∈ U_δ(p ₀)⊂\T³ is proven. Moreover, the analyticity of associated eigenfunction is shown.

Citations

• Exotic atom pairs: Repulsively bound states in an optical lattice

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