Below-threshold effects for the two particle discrete Schr¨odinger operator on a lattice
Year: 2025
Type: article
Abstract: We consider the family of Schrödinger operators Hγλ(K), which are associated with the Hamiltonian of a system of two identical bosons on the d-dimensional lattice Zd, where d≥3, with interactions on each site and between nearest-neighbor sites with strengths γ∈R− and λ∈R−, respectively. Here, K∈Td is a fixed quasi-momentum of the particles. We first partition the (γ,λ)−plane into connected components S0, S1 and Cj,j=0,1,2. Further, we establish below-threshold effects for Hγλ(0) on the boundaries of the connected components ∂S0 and ∂Cj,j=0,2.
Source: Russian Mathematics
Authors: I. N. Bozorov, Sh. I. Khamidov
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4415079783