Local enhancement of the mean-field approximation for bosons
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915069782130688 |
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| author | Lemm, Marius Rademacher, Simone Zhang, Jingxuan |
| author_facet | Lemm, Marius Rademacher, Simone Zhang, Jingxuan |
| contents | We study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive distance $ρ>0$ from the initial BEC, the mean-field approximation error at time $t\leq ρ/v$ is bounded as $ρ^{-n}$, for arbitrarily large $n\geq 1$. This is a consequence of new ballistic propagation bounds on the fluctuations around the condensate. To prove this, we develop a variant of the ASTLO (adiabatic spacetime localization observable) method for the particle non-conserving generator of the fluctuation dynamics around Hartree states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local enhancement of the mean-field approximation for bosons Lemm, Marius Rademacher, Simone Zhang, Jingxuan Mathematical Physics Analysis of PDEs 82C10, 35Q40, 35Q55, 81V73, 81V70 We study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive distance $ρ>0$ from the initial BEC, the mean-field approximation error at time $t\leq ρ/v$ is bounded as $ρ^{-n}$, for arbitrarily large $n\geq 1$. This is a consequence of new ballistic propagation bounds on the fluctuations around the condensate. To prove this, we develop a variant of the ASTLO (adiabatic spacetime localization observable) method for the particle non-conserving generator of the fluctuation dynamics around Hartree states. |
| title | Local enhancement of the mean-field approximation for bosons |
| topic | Mathematical Physics Analysis of PDEs 82C10, 35Q40, 35Q55, 81V73, 81V70 |
| url | https://arxiv.org/abs/2412.13868 |