Dynamics of mean-field Fermi systems with nonzero pairing
Abstract
We study the dynamics of many-body Fermi systems, for a class of initial data which are close to quasi-free states exhibiting a nonvanishing pairing matrix. We focus on the mean-field scaling, which for fermionic systems is naturally coupled with a semiclassical scaling. Under the assumption that the initial datum enjoys a suitable semiclassical structure, we give a rigorous derivation of the time-dependent Hartree-Fock-Bogoliubov equation, a nonlinear effective evolution equation for the one-particle density matrix of the system, as the number of particles goes to infinity. Our result holds for all macroscopic times, and provides bounds for the rate of convergence.
Cite
@article{arxiv.2310.15280,
title = {Dynamics of mean-field Fermi systems with nonzero pairing},
author = {Stefano Marcantoni and Marcello Porta and Julien Sabin},
journal= {arXiv preprint arXiv:2310.15280},
year = {2024}
}
Comments
v1 43 pages; v2 minor changes, references added, 44 pages; v3 minor corrections, 46 pages