Bound States of a Lattice Two-Boson System with Interactions up to the Next Neighboring Sites

We study the family , of discrete Schrödinger operators, associated to the Hamiltonian of a system of two identical bosons on the two-dimensional lattice interacting through on one site, nearest-neighbour sites and next-nearest-neighbour sites with interaction magnitudes and respectively. We prove t...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2024-07, Vol.45 (7), p.3323-3332
Main Authors: Lakaev, S. N., Sharipova, S. F.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Bosons
Eigenvalues
Geometry
Lower bounds
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Probability Theory and Stochastic Processes
Schrodinger equation
Subspaces
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Summary:We study the family , of discrete Schrödinger operators, associated to the Hamiltonian of a system of two identical bosons on the two-dimensional lattice interacting through on one site, nearest-neighbour sites and next-nearest-neighbour sites with interaction magnitudes and respectively. We prove there existence an invariant subspace of the operator that its restriction on this subspace has only one simple eigenvalue, which lay below or above of its essential spectrum depending on the interaction magnitude . Applying this result we give a lower bound for the number of the discrete eigenvalues of the operator for all .
ISSN:1995-0802
1818-9962
DOI:10.1134/S199508022460403X