Saved in:
Bibliographic Details
Main Authors: Benedikter, Niels, Boccato, Chiara, Monaco, Domenico, Nguyen, Ngoc Nhi
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.16001
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • We study the quantum dynamics of a large number of interacting fermionic particles in a constant magnetic field. In a coupled mean-field and semiclassical scaling limit, we show that solutions of the many-body Schrödinger equation converge to solutions of a non-linear Hartree-Fock equation. The central ingredient of the proof are certain semiclassical trace norm estimates of commutators of the position and momentum operators with the one-particle density matrix of the solution of the Hartree-Fock equation. In a first step, we prove their validity for non-interacting initial data in a magnetic field by generalizing a 2020 result of Fournais and Mikkelsen. We then propagate these bounds from the initial data along the Hartree-Fock flow to arbitrary times.