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Equilibrium and nonequilibrium entanglement properties of 2D and 3D Fermi gases

We investigate the entanglement properties of the equilibrium and nonequilibrium quantum dynamics of 2D and 3D Fermi gases, by computing entanglement entropies of extended space regions, which generally show multiplicative logarithmic corrections to the leading power-law behaviors, corresponding to the logarithmic corrections to the area law. We consider 2D and 3D Fermi gases of N particles constrained within a limited space region, for example by a hard-wall trap, at equilibrium at T=0, i.e. in their ground state, and compute the first few terms of the asymptotic large-N behaviors of entanglement entropies and particle fluctuations of subsystems with some convenient geometries, which allow us to significantly extend their computation. Then, we consider their nonequilibrium dynamics after instantaneously dropping the hard-wall trap, which allows the gas to expand freely. We compute the time dependence of the von Neumann entanglement entropy of space regions around the original trap. We show that at small time it is characterized by the relation $S \approx π^2 V/3$ with the particle variance, and multiplicative logarithmic corrections to the leading power law, i.e. $S \sim t^{1-d}\ln(1/t)$.