Effective Dynamics of Extended Fermi Gases in the High-Density Regime

We study the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. We consider both particles with non-relativistic and with relativistic dispersion. We focus on the high-density regime, in the semiclassical scaling, and we consider a class of initial data describing zero-temperature states. In the non-relativistic case 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 relativistic dispersion, we show convergence of the many-body evolution to the relativistic Hartree equation for 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 us to study the quantum dynamics of extensive many-body Fermi gases.

Automated summary

This study investigates the quantum evolution of many-body Fermi gases in three dimensions, considering both non-relativistic and relativistic dispersion particles. The focus is on the high-density regime and a class of initial data describing zero-temperature states. In the non-relativistic case, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation in short macroscopic times as the density approaches infinity. In the case of relativistic dispersion, the many-body evolution converges to the relativistic Hartree equation for all macroscopic times. The rate of convergence depends only on the density, allowing for the study of extensive many-body Fermi gases' quantum dynamics.