On the existence of the N-body Efimov effect

Abstract

In this paper, we prove the existence of the Efimov effect for N-body quantum systems with N⩾4. Under the conditions that the bottom of the essential spectrum, E 0, of the N-body operator is attained by the spectra of a unique three-cluster Subhamiltonian and its three associated two-cluster Subhamiltonians, and that at least two of these two-cluster Subhamiltonians have a resonance at the threshold E 0, we give a lower bound of the form C 0|log( E 0− λ)| for the number of eigenvalues on the left of λ, λ<E 0 , where C 0 is a positive constant depending only on the reduced masses in the three-cluster decomposition. We also obtain a lower bound on the number of discrete eigenvalues in coupling constant perturbation.