Discrete Spectrum of a Model Operator Related to Three-Particle Discrete Schrödinger Operators

Abstract

A model operator $H_{\mu },$ $\mu >0$ associated to a system of three particles on the three-dimensional lattice ${\mathbb{Z}}^3$ that interact via nonlocal pair potentials is considered. We study the case where the parameter function $w$ has a special form with the non degenerate minimum at the $n,n>1$ points of the six-dimensional torus ${\mathbb{T}}^6.$ If the associated Friedrichs model has a zero energy resonance, then we prove that the operator $H_{\mu }$ has infinitely many negative eigenvalues accumulating at zero and we obtain an asymptotics for the number of eigenvalues of $H_{\mu }$ lying below $z,$ $z<0$ as $z\to -0.$

11 pages

References in corpus (1)

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