Dynamics of Mean-Field Fermi Systems with Nonzero Pairing
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.
Authors
- Julien Sabin
- Stefano Marcantoni (ORCID: https://orcid.org/0000-0002-0525-5884)
- Marcello Porta (ORCID: https://orcid.org/0000-0002-7725-8398)
Institutions
- Scuola Internazionale Superiore di Studi Avanzati (IT)
- Université Rennes 2 (FR)
- Institut de Biologie Valrose (FR)
- Institut de recherche mathématique de Rennes (FR)
- Université de Rennes (FR)
Publication Details
- Journal
- Annales Henri Poincaré
- Published
- 2024-09-28
- DOI
- https://doi.org/10.1007/s00023-024-01473-8
- Citations
- 1
- Primary Topic
- Cold Atom Physics and Bose-Einstein Condensates
- Type
- article
- Field-Weighted Citation Impact
- 0.34
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Scuola Internazionale Superiore di Studi Avanzati
- European Commission
- Gruppo Nazionale per la Fisica Matematica
- European Research Council
- H2020 Marie Skłodowska-Curie Actions