DISCRETE SPECTRUM OF TWO-FERMION SCHRÖDINGER OPERATORS ON 3D LATTICES - Abdukhakimov, Saidakbar; Khasanov, Atxam (Scientific practical conference, 2026)
This thesis investigates the spectral properties of two-fermion Schrödinger operators on the three-dimensional lattice with nearest- and next-nearest-neighbor interactions. We focus on the discrete eigenvalues lying outside the essential spectrum and analyze their dependence on interaction parameters. The study employs decomposition into invariant subspaces and Fredholm determinant techniques to characterize bound states and critical phenomena.