Low energy effects for a family of Friedrichs models

Sergio Albeverio; Saidakhmat N. Lakaev; Ramiza Kh. Djumanova

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Low energy effects for a family of Friedrichs models

Sergio Albeverio·Saidakhmat N. Lakaev·Ramiza Kh. Djumanova

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Abstract

A family of Friedrichs models with rank one perturbations $h_μ(p),$ $p \in (-π,π]^3,μ>0$ associated to a system of two particles on the lattice $\Z^3$ is considered. The existence of a unique strictly positive eigenvalue below the bottom of the essential spectrum of $h_μ(p)$ for all nontrivial values $p \in (-π,π]^3$ under the assumption that $h_μ(0)$ has either a zero energy resonance (virtual level) or a threshold eigenvalue is proved. Low energy asymptotic expansion for the Fredholm determinant associated to family of Friedrichs models is obtained.

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BibTeX RIS

Sergio Albeverio, Saidakhmat N. Lakaev, Ramiza Kh. Djumanova. 2006-04-12. Low energy effects for a family of Friedrichs models. https://arxiv.org/abs/math/0604282

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