Large-scale limits of interacting particle systems

Collection Large-scale limits of interacting particle systems

Organizer(s) Mitia Duerinckx, Sergio Simonella, and Raphael Winter
Date(s) 04/10/2021 - 08/10/2021
linked URL'21.html
00:00:00 / 00:00:00
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Correlation energy of a weakly interacting Fermi gas

By Marcello Porta

In this talk I will discuss the ground state properties of homogeneous, interacting Fermi gases, in the mean-field regime. In this regime, Hartree-Fock theory provides a good approximation for the ground state energy of the system; this approximation is based on the replacement of the space of fermionic wave functions with the smaller set of Slater determinants, where the only correlations among the particles are those induced by the Pauli principle. I will discuss a rigorous approach that allows to go beyond the Hartree-Fock approximation, and that in particular allows to compute the leading order of the correlation energy, defined as the difference between the many-body and Hartree-Fock ground state energies. The expression we obtain reproduces the ground state energy of a non-interacting Bose gas, and agrees with the prediction of the random-phase approximation. The proof is based on a rigorous bosonization method, that allows to describe the particle-hole excitations around the Fermi surface in terms of a quasi-free Bose gas. Joint work with N. Benedikter, P. T. Nam, B. Schlein and R. Seiringer.

Information about the video

  • Date of recording 06/10/2021
  • Date of publication 12/10/2021
  • Institution IHES
  • Language English
  • Director(s) Mandarine Audiovisuel
  • Format MP4

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