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On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas
Abstract
This paper is devoted to the dynamics of a weakly interacting Fermi gas at the kinetic time regime t∼ λ−2 where λ≪ 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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BibTeX
@misc{madsen2026asymptotic,
title = {{On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas}},
author = {Peter S. Madsen and Phan Thành Nam and Herbert Spohn and Minh-Binh Tran},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.13499},
eprint = {2605.13499},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.13499},
}
RIS
TY - UNPB
TI - On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas
AU - Peter S. Madsen
AU - Phan Thành Nam
AU - Herbert Spohn
AU - Minh-Binh Tran
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2605.13499
UR - https://arxiv.org/abs/2605.13499
AB - This paper is devoted to the dynamics of a weakly interacting Fermi gas at the kinetic time regime t∼ λ^−2 where λ≪ 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.
ER -