Asymptotics of the discrete spectrum of a model operator associated with a system of three particles on a lattice

摘要

We consider a model Schr?dinger operator H_μ associated with a system of three particles on the threedimensional lattice ?~3 with a functional parameter of special form. We prove that if the corresponding Friedrichs model has a zero-energy resonance, then the operator H_μ has infinitely many negative eigenvalues accumulating at zero (the Efimov effect). We obtain the asymptotic expression for the number of eigenvalues of H_μ below z as z → -0.