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arXiv · 2605.13499

On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas

Peter S. Madsen·Phan Thành Nam·Herbert Spohn·Minh-Binh Tran
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Abstract

This paper is devoted to the dynamics of a weakly interacting Fermi gas at the kinetic time regime $t\sim \lambda^{-2}$ where $\lambda \ll 1$ 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.

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Peter S. Madsen, Phan Thành Nam, Herbert Spohn, Minh-Binh Tran. 2026-05-13. On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas. https://arxiv.org/abs/2605.13499

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