On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914563373400064 |
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| author | Madsen, Peter S. Nam, Phan Thành Spohn, Herbert Tran, Minh-Binh |
| author_facet | Madsen, Peter S. Nam, Phan Thành Spohn, Herbert Tran, Minh-Binh |
| contents | This paper is devoted to the dynamics of a weakly interacting Fermi gas at the kinetic time regime $t\sim λ^{-2}$ where $λ\ll 1$ is the strength of the interaction potential. We prove that if the initial state is close to equilibrium, then the two-point time correlation function of the many-body quantum dynamics can be computed effectively. In fact, we show that its leading order behavior is determined completely by the collisional frequency of the Boltzmann-Nordheim collision operator at equilibrium. This settles a prediction by Lukkarinen-Spohn, and thus gives a justification of the quantum Boltzmann equation from many-body quantum mechanics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_13499 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas Madsen, Peter S. Nam, Phan Thành Spohn, Herbert Tran, Minh-Binh Mathematical Physics 82B10, 81V74, 82B40 This paper is devoted to the dynamics of a weakly interacting Fermi gas at the kinetic time regime $t\sim λ^{-2}$ where $λ\ll 1$ is the strength of the interaction potential. We prove that if the initial state is close to equilibrium, then the two-point time correlation function of the many-body quantum dynamics can be computed effectively. In fact, we show that its leading order behavior is determined completely by the collisional frequency of the Boltzmann-Nordheim collision operator at equilibrium. This settles a prediction by Lukkarinen-Spohn, and thus gives a justification of the quantum Boltzmann equation from many-body quantum mechanics. |
| title | On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas |
| topic | Mathematical Physics 82B10, 81V74, 82B40 |
| url | https://arxiv.org/abs/2605.13499 |