Searcharxiv⌕ Search

arXiv subjects

Peter S. Madsen

Publications and source records attributed to Peter S. Madsen.

4 recordsLinked to original sources
arXiv2026

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

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.

math-ph↗
arXiv2019

Semi-classical limit of confined fermionic systems in homogeneous magnetic fields

We consider a system of $ N $ interacting fermions in $ \mathbb{R}^3 $ confined by an external potential and in the presence of a homogeneous magnetic field. The intensity of the interaction has the mean-field scaling $ 1/N $. With a semi-classical parameter $ \hbar \sim N^{-1/3} $, we prove convergence in the large $ N $ limit to the appropriate Magnetic Thomas-Fermi type model with various strength scalings of the magnetic field.

math-ph↗
arXiv2019

Semi-classical limit of large fermionic systems at positive temperature

We study a system of $N$ interacting fermions at positive temperature in a confining potential. In the regime where the intensity of the interaction scales as $1/N$ and with an effective semi-classical parameter $\hbar=N^{-1/d}$ where $d$ is the space dimension, we prove the convergence to the corresponding Thomas-Fermi model at positive temperature.

math-ph↗