Скачать или смотреть Marcello Porta: On the correlation energy of interacting fermionic systems in the mean-field regime

The lecture was held within the of the Hausdorff Junior Trimester Program: Kinetic Theory

Abstract:
In this talk I will discuss the ground state properties of a homogeneous, interacting Fermi gas, in the mean-field regime. In particular, I will focus on the correlation energy, defined as the difference between many-body and Hartree-Fock ground state energies. Recently, progress has been made in the rigorous understanding of the precise value of this quantity. I will present an upper bound for the correlation energy that agrees with an old prediction of Gell-Mann and Brueckner in the physics literature, whose proof is based on a rigorous bosonization technique. Then, I will discuss a lower bound, matching the upper bound for small interaction potentials.
The upper bound is based on a joint work with N. Benedikter, P. T. Nam, B. Schlein and R. Seiringer, while the lower bound is based on a joint work with C. Hainzl and F. Rexze.