The existence of bound states in a system of three particles in an optical lattice

Abstract

We consider the hamiltonian ${\mathrm{H}}_{\mu },\mu \in \mathbb{R}$ of a system of three-particles (two identical fermions and one different particle) moving on the lattice ${\mathbb{Z}}^d,d=1,2$ interacting through repulsive $(\mu >0)$ or attractive $(\mu <0)$ zero-range pairwise potential $\mu V$. We prove for any $\mu \ne 0$ 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 ${\mathrm{H}}_{\mu }$.

15 pages. arXiv admin note: substantial text overlap with arXiv:1512.01983; text overlap with arXiv:cond-mat/0605196 by other authors

References in corpus (1)

• Repulsively bound atom pairs in an optical lattice

Cited by in corpus (2)

• Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions
• Correlated dynamics of three-particle bound states induced by emergent impurities in Bose-Hubbard model