The threshold effects for a family of Friedrichs models under rank one perturbations

2006/04/12 by Sergio Albeverio, Albeverio, Sergio, Saidakhmat N. Lakaev +3 · 1 citation
Mathematics · Physics and Astronomy · #47N50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 81Q10 #Secondary: 35P20 #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35P20 #msc:47N50 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.math/0604277

15 pages

arxiv created 2006/08/14 · arxiv updated 2009/12/01

Abstract

A family of Friedrichs models under rank one perturbations h_μ(p), p ∈ (-π,π]³, μ>0, associated to a system of two particles on the three dimensional lattice \Z³ is considered. We prove the existence of a unique eigenvalue below the bottom of the essential spectrum of h_μ(p) for all nontrivial values of p under the assumption that h_μ(0) has either a threshold energy resonance (virtual level) or a threshold eigenvalue. The threshold energy expansion for the Fredholm determinant associated to a family of Friedrichs models is also obtained.

Cited by

• Threshold Resonances, Critical Couplings, and Eigenvalue Bounds for Two-Particle Operators on ℤ³

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