arXiv:2310.15280 · Annales Henri Poincaré

Dynamics of Mean-Field Fermi Systems with Nonzero Pairing

Stefano Marcantoni, Marcello Porta, Julien Sabin

Published Sep 28, 2024• 1 citation

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 generalized 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.

DOI: 10.1007/s00023-024-01473-8

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