On the effective dynamics of Bose-Fermi mixtures
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913923211460608 |
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| author | Cárdenas, Esteban Miller, Joseph K. Pavlović, Nataša |
| author_facet | Cárdenas, Esteban Miller, Joseph K. Pavlović, Nataša |
| contents | In this work, we describe the dynamics of a Bose-Einstein condensate interacting with a degenerate Fermi gas, at zero temperature. First, we analyze the mean-field approximation of the many-body Schrödinger dynamics and prove emergence of a coupled Hartree-type system of equations. We obtain rigorous error control that yields a non-trivial scaling window in which the approximation is meaningful. Second, starting from this Hartree system, we identify a novel scaling regime in which the fermion distribution behaves semi-clasically, but the boson field remains quantum-mechanical; this is one of the main contributions of the present article. In this regime, the bosons are much lighter and more numerous than the fermions. We then prove convergence to a coupled Vlasov-Hartee system of equations with an explicit convergence rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the effective dynamics of Bose-Fermi mixtures Cárdenas, Esteban Miller, Joseph K. Pavlović, Nataša Mathematical Physics Analysis of PDEs 35Q40 35Q41 35Q49 35Q82 81V73 81V74 82C10 82D05 In this work, we describe the dynamics of a Bose-Einstein condensate interacting with a degenerate Fermi gas, at zero temperature. First, we analyze the mean-field approximation of the many-body Schrödinger dynamics and prove emergence of a coupled Hartree-type system of equations. We obtain rigorous error control that yields a non-trivial scaling window in which the approximation is meaningful. Second, starting from this Hartree system, we identify a novel scaling regime in which the fermion distribution behaves semi-clasically, but the boson field remains quantum-mechanical; this is one of the main contributions of the present article. In this regime, the bosons are much lighter and more numerous than the fermions. We then prove convergence to a coupled Vlasov-Hartee system of equations with an explicit convergence rate. |
| title | On the effective dynamics of Bose-Fermi mixtures |
| topic | Mathematical Physics Analysis of PDEs 35Q40 35Q41 35Q49 35Q82 81V73 81V74 82C10 82D05 |
| url | https://arxiv.org/abs/2309.04638 |