Threshold Resonances, Critical Couplings, and Eigenvalue Bounds for Two-Particle Operators on ${\mathbb{Z}}^3$

Saidakhmat N. Lakaev, Saidakbar S. Abduvayitov, Shuhrat S. Lakaev

We study a family of lattice Schrödinger operators $H_{\hat{I}{¼}_1\hat{I}{¼}_2}(K)$ describing two identical bosons on the three-dimensional cubic lattice ${\mathbb{Z}}^3$, where $K \in \mathbb{T}…