The existence of an isolated band in a system of three particles in an optical lattice

Abstract

We prove the existence of two-and three-particle bound states of the Schrödinger operators $h_μ(k),k\in \T^d$ and $H_μ(K),K\in \T^d$ associated to Hamiltonians ${\mathrm{h}}_{\mu }$ and ${\mathrm{H}}_{\mu }$ of a system of two and three identical bosons on the lattice ${\mathbb{Z}}^d,d=1,2$ interacting via pairwise zero-range attractive $\mu <0$ or repulsive $\mu >0$ potentials. As a consequence we show the existence of an isolated band in the two and three bosonic systems in an optical lattice.

14 pages. arXiv admin note: text overlap with arXiv:1508.07581