The existence of bound states in a system of three particles in an optical lattice
We consider the hamiltonian $\mathrm{H}_μ,μ\in \R$ of a system of three-particles (two identical fermions and one different particle) moving on the lattice ${\Z}^d ,\, d=1,2 $ interacting through repulsive $(μ>0)$ or attractive $(μ<0)$ zero-range pairwise potential $μV$. We prove for any $μ\ne0$ the existence of bound state of the discrete three-particle Schrödinger operator $H_μ(K),\,K\in \T^d$ being the three-particle quasi-momentum, associated to the hamiltonian $\mathrm{H}_μ$.
math.SP↗