Universal Dynamics of a Spin-$3/2$ Fermi Gas in Traps with Distinct Spectra

Abstract: Universal power-law decay of spin-mixing oscillations has been observed in a harmonically trapped spin-$3/2$ Fermi gas, whose exactly equally spaced spectrum represents a highly special case. To gain insight into the origin of this behavior, we investigate the dynamics in traps with increasing and decreasing level spacings, represented by the infinite square well and the Pöschl--Teller potential, respectively. Despite pronounced differences in their single-particle spectra, all systems exhibit power-law decay of coherent oscillations, described by $A(t) = A_{0} - γt<sup>α$. The exponent $α$ remains insensitive to particle number, interaction strength, and the overall energy scale, but exhibits systematic differences among traps with distinct spectral structures. In contrast, the decay parameter $γ$ is strongly influenced by both the spectral structure and the overall energy scale. These findings demonstrate that power-law decay is not restricted to the harmonic trap but persists across qualitatively distinct spectral structures. The observed variation of $α$ among different traps further suggests that the underlying single-particle spectrum plays an important role in shaping the decay dynamics.