Existence of bound states of N-body problem in an optical lattice

Abstract

We provide sufficient conditions to have at least one N -particle bound state below the essential spectrum of a large class of N -particle discrete Schrödinger operators H(K), K ∈ T d , d ≥ 1, associated to the Hamiltonian of (not necessarily identical) N particles, moving on a lattice Z d and interacting via short-range pair potentials. We also describe the essential spectrum of H(K).Key words and phrases. Schrödinger operator -dispersion functions -short-range pair potentials -HVZ theorem -essential spectrum -cluster operators -bound states.