Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institution: Texas A&M University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161155827