The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915419059650560 |
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| author | Lampart, Jonas Triay, Arnaud |
| author_facet | Lampart, Jonas Triay, Arnaud |
| contents | We study a dilute system of $N$ interacting bosons coupled to an impurity particle via a pair potential in the Gross--Pitaevskii regime. We derive an expansion of the ground state energy up to order one in the boson number, and show that the difference of excited eigenvalues to the ground state is given by the eigenvalues of the renormalized Bogoliubov--Fröhlich Hamiltonian in the limit $N\to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime Lampart, Jonas Triay, Arnaud Mathematical Physics Quantum Gases 81V73 We study a dilute system of $N$ interacting bosons coupled to an impurity particle via a pair potential in the Gross--Pitaevskii regime. We derive an expansion of the ground state energy up to order one in the boson number, and show that the difference of excited eigenvalues to the ground state is given by the eigenvalues of the renormalized Bogoliubov--Fröhlich Hamiltonian in the limit $N\to \infty$. |
| title | The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime |
| topic | Mathematical Physics Quantum Gases 81V73 |
| url | https://arxiv.org/abs/2401.14911 |