MCS-MP Seminar: Marcello Porta

Speaker: Marcello Porta, SISSA, Italy

Title: Dynamics of high density Fermi gases

Abstract:  I will discuss the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. I will focus on the high-density regime, and I will consider a class of initial data describing zero-temperature states with a suitable local semiclassical structure. We prove that, as the density goes to infinity, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation, for short macroscopic times. In the case of a pseudo-relativistic dispersion, the result extends to all macroscopic times. With respect to previous work, the rate of convergence does not depend on the total number of particles, but only on the density: in particular, our result allows to study the dynamics of many-body Fermi gases in the thermodynamic limit. Joint work with Luca Fresta and Benjamin Schlein.