Universal behaviors of dynamical quantum transition in trapped large spin fermions

Dynamical universality in far-from-equilibrium quantum systems has already attracted significant attention. We have performed a systematic study on the long-time spin-mixing dynamics of harmonically trapped spin-$3/2$ Fermi gases by solving the time-dependent Hartree–Fock equations. Our findings reveal that the evolution process goes through two distinct stages, both of which exhibit interesting universal behaviors. In the beginning, the so-called giant oscillation is observed, with the amplitude damping in a universal power-law, $A\left(t\right)=A_0-\gamma t^{\alpha }$, where the exponent $\alpha$ remains constant regardless of the particle number and interaction strength. Then a revival-like phenomenon appears in the long-time stage, with the oscillation amplitude increasing suddenly and soon decreasing again. Differently, the damping seems in an exponential-law, $A\left(t^{\prime }\right)=A_0^{\prime }+k{exp}^{-\beta t^{\prime }}$, where the parameter $\beta$ depends on both the particle number and interaction strength. Such difference indicates that the second stage is not a simple revival of the first one, which implies that a dynamical quantum transition occurs between the two stages.