A two-boson lattice Hamiltonian with interactions up to next-neighboring sites
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913539451518976 |
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| author | Lakaev, S. N. Motovilov, A. K. Akhmadova, M. O. |
| author_facet | Lakaev, S. N. Motovilov, A. K. Akhmadova, M. O. |
| contents | A system of two identical spinless bosons on the two-dimensional lattice is considered under the assumption that on-site and first and second nearest-neighboring site interactions between the bosons are only nontrivial and that these interactions are of magnitudes $γ$, $λ$, and $μ$, respectively. A partition of the $(γ,λ,μ)$-space into connected components is established such that, in each connected component, the two-boson Schroedinger operator corresponding to the zero quasi-momentum of the center of mass has a definite (fixed) number of eigenvalues, which are situated below the bottom of the essential (continuous) spectrum and above its top. Moreover, for each connected component, a sharp lower bound is established on the number of isolated eigenvalues for the two-boson Schrödinger operator corresponding to any admissible nonzero value of the center-of-mass quasimomentum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07070 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A two-boson lattice Hamiltonian with interactions up to next-neighboring sites Lakaev, S. N. Motovilov, A. K. Akhmadova, M. O. Mathematical Physics Quantum Physics A system of two identical spinless bosons on the two-dimensional lattice is considered under the assumption that on-site and first and second nearest-neighboring site interactions between the bosons are only nontrivial and that these interactions are of magnitudes $γ$, $λ$, and $μ$, respectively. A partition of the $(γ,λ,μ)$-space into connected components is established such that, in each connected component, the two-boson Schroedinger operator corresponding to the zero quasi-momentum of the center of mass has a definite (fixed) number of eigenvalues, which are situated below the bottom of the essential (continuous) spectrum and above its top. Moreover, for each connected component, a sharp lower bound is established on the number of isolated eigenvalues for the two-boson Schrödinger operator corresponding to any admissible nonzero value of the center-of-mass quasimomentum. |
| title | A two-boson lattice Hamiltonian with interactions up to next-neighboring sites |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2410.07070 |