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

2015/12/07 by Dell'Antonio, Gianfausto, Lakaev, Saidakhmat N., Khalkhuzhaev, Ahmad M.
#47N50 #FOS: Mathematics #Primary: 81Q10 #Secondary: 35P20 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1512.01983

Abstract

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

Related

• Existence of bound states of N-body problem in an optical lattice
• Number of bound states of the Hamiltonian of a lattice two-boson system with interactions up to the next neighbouring sites
• Large effective three-body interaction in a double-well optical lattice
• The number and location of two particle Schrödinger operators on a lattice
• On the structure of the essential spectrum of the three-particle Schrödinger operators on a lattice