Seminar Analysis and Mathematical Physics: Marcello Porta (SISSA)

Dynamics of mean-field Fermi systems with nonzero pairing

I will discuss the dynamics of many-body Fermi gases, in the mean-field regime. I will consider a class of initial data which are close enough to quasi-free states, with a non-zero pairing matrix. Assuming a suitable semiclassical structure for the initial datum, expected to hold at low enough energy and that we can establish for translation-invariant states, I will present a theorem that shows that the many-body evolution of the system can be well approximated by the Hartree-Fock-Bogoliubov equation, a non-linear effective evolution equation describing the coupled dynamics of the reduced one-particle density matrix and of the pairing matrix. Joint work with Stefano Marcantoni (Nice) and Julien Sabin (Rennes).

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