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Pré-Publication, Document De Travail Année : 2023

Dynamics of mean-field Fermi systems with nonzero pairing

Résumé

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.
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Dates et versions

hal-04378513 , version 1 (08-01-2024)

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  • HAL Id : hal-04378513 , version 1

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Stefano Marcantoni, Marcello Porta, Julien Sabin. Dynamics of mean-field Fermi systems with nonzero pairing. 2023. ⟨hal-04378513⟩
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