Low energy effects for a family of Friedrichs models

Abstract

A family of Friedrichs models with rank one perturbations $h_{\mu }(p),$ $p\in (-\pi ,\pi {]}^3,\mu >0$ associated to a system of two particles on the lattice ${\mathbb{Z}}^3$ is considered. The existence of a unique strictly positive eigenvalue below the bottom of the essential spectrum of $h_{\mu }(p)$ for all nontrivial values $p\in (-\pi ,\pi {]}^3$ under the assumption that $h_{\mu }(0)$ 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.

11 pages

References in corpus (1)

• Comment on the article "On the Existence of the N-Body Efimov Effect" by X. P. Wang