On the existence of the N-body Efimov effect

In this paper, we study a generalization of the Efimov effect for three-body Schrödinger operators to N -body ones with N ≥ 4. We prove the infiniteness of the discrete spectrum under the conditions that the bottom of the essential spectrum, E0, is only attained by the spectra of a unique three-cluster Subhamiltonian and its three associated two-clusters Subhamiltonians, and that at least two of these two-cluster Subhamiltonians have a resonance at E0. We give a lower bound on the number of eigenvalues of the form C0| log |λ − E0||, when λ tends to E0. Here C0 is a positive constant depending only on the reduced masses in the three-cluster decomposition.