Dynamics of mean-field Fermi systems with nonzero pairing
arXiv:2310.15280 · doi:10.1007/s00023-024-01473-8
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.
v1 43 pages; v2 minor changes, references added, 44 pages; v3 minor corrections, 46 pages
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