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

Sergio Albeverio·Saidakhmat N. Lakaev·Zahriddin I. Muminov
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Abstract

A family of Friedrichs models under rank one perturbations $h_μ(p),$ $p \in (-π,π]^3$, $μ>0,$ associated to a system of two particles on the three dimensional lattice $\Z^3$ 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.

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Sergio Albeverio, Saidakhmat N. Lakaev, Zahriddin I. Muminov. 2006-08-14. The threshold effects for a family of Friedrichs models under rank one perturbations. https://arxiv.org/abs/math/0604277

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