Derivation of Hartree theory for two-dimensional attractive Bose gases in almost Gross-Pitaevskii regime
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| Format: | Preprint |
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2024
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| _version_ | 1866912627780747264 |
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| author | Junge, Lukas Visconti, François Louis Antoine |
| author_facet | Junge, Lukas Visconti, François Louis Antoine |
| contents | We study the ground state energy of trapped two-dimensional Bose gases with mean-field type interactions that can be attractive. We prove the stability of second kind of the many-body system and the convergence of the ground state energy per particle to that of a non-linear Schrödinger (NLS) energy functional. Notably, we can take any polynomial scaling of the interaction, and even exponential scalings arbitrarily close to the Gross--Pitaevskii regime, which is a drastic improvement on the best-known result for systems with attractive interactions. As a consequence of the stability of second kind we also obtain Bose-Einstein condensation for the many-body ground states for a much improved range of the diluteness parameter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_23150 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivation of Hartree theory for two-dimensional attractive Bose gases in almost Gross-Pitaevskii regime Junge, Lukas Visconti, François Louis Antoine Mathematical Physics We study the ground state energy of trapped two-dimensional Bose gases with mean-field type interactions that can be attractive. We prove the stability of second kind of the many-body system and the convergence of the ground state energy per particle to that of a non-linear Schrödinger (NLS) energy functional. Notably, we can take any polynomial scaling of the interaction, and even exponential scalings arbitrarily close to the Gross--Pitaevskii regime, which is a drastic improvement on the best-known result for systems with attractive interactions. As a consequence of the stability of second kind we also obtain Bose-Einstein condensation for the many-body ground states for a much improved range of the diluteness parameter. |
| title | Derivation of Hartree theory for two-dimensional attractive Bose gases in almost Gross-Pitaevskii regime |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2410.23150 |