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We investigate the particle-number dependence of some features of theout-of-equilibrium dynamics of d-dimensional Fermi gases in the dilute regime.We consider protocols entailing the variation of the external potential whichconfines the particles within a limited spatial region, in particular suddenchanges of the trap size. In order to characterize the dynamic behavior of theFermi gas, we consider various global quantities such as the ground-statefidelity for different trap sizes, the quantum work statistics associated withthe protocol considered, and the Loschmidt echo measuring the overlap of theout-of-equilibrium quantum states with the initial ground state. Theirasymptotic particle-number dependences show power laws for noninteracting Fermigases. We also discuss the effects of short-ranged interactions to the powerlaws of the average work and its square fluctuations, within the Hubbard modeland its continuum limit, arguing that they do not generally change theparticle-number power laws of the free Fermi gases, in any spatial dimensions.

Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps