Nonthermal Dynamics and Scar-Like Spectral Structures in a High-Spin Fermi Gas

Abstract

We investigate nonequilibrium dynamics and weak ergodicity breaking in a harmonically trapped spin-$3/2$ Fermi gas by using the time-dependent Hartree-Fock equation. The Shannon entropy remains bounded and oscillatory throughout the evolution, indicating restricted and nonuniform exploration of Hilbert space rather than immediate thermalization. The fidelity exhibits pronounced, nearly periodic revivals whose period is largely insensitive to particle number and interaction strength, while the revival amplitude gradually decreases with increasing system size and interaction strength. The Fourier spectrum of the fidelity reveals a set of sharp and approximately equally spaced peaks. By projecting the time-evolved state onto the instantaneous eigenbasis of the self-consistent mean-field Hamiltonian, we identify a sparse and spectrally stable manifold that forms a quasi-regular energy ladder, with spacing comparable to the dominant quasienergy interval extracted from the fidelity spectrum. These results indicate that the long-lived coherent oscillations originate from collective phase interference associated with a quasi-regular spectral structure embedded in the many-body continuum, rather than from a conventional eigenstate-dominated scar mechanism.

Figures (6)

• Figure 1: Nonthermal spin-mixing dynamics and Shannon entropy. Time evolution of relative populations $n_m(t)$ for $m = \pm1/2$ ( a), where $\Delta T$ is the oscillation period, and the corresponding Shannon entropy $S(t)$ ( b). The particle number is $N=40$, with interactions $c_0=1.0$ and $c_2=0.1$.
• Figure 2: Fidelity dynamics and its coherence revivals.a The fidelity exhibits pronounced periodic revivals at early times (Stage I). At later times (Stage II), the envelope of the fidelity decays slowly. b is an enlarged version of a part of a, where $\Delta t$ is the revival period. c Fidelity dynamics of an initial state constructed by independent phase randomization of each occupied single-particle orbital and spin component. The particle number is $N=40$, with interactions $c_0=1.0$ and $c_2=0.1$.
• Figure 3: Time evolution of the fidelity $P(t)$ for different system parameters in Stage-I.a Comparison of systems with particle numbers $N=20$ (green dashed line) and $N=100$ (blue line). The interactions are set to $c_0=1.0$ and $c_2=0.1$. b Comparison of different interaction strengths $c_0=1.0$ (red dotted line) and $c_0=2.0$ (black line), for a fixed particle number $N=40$ and non-mixing interaction strength $c_2=0.1$.
• Figure 4: The fidelity density of the first revival peak. For each particle number $N$, we extract the first prominent revival maximum $P(T_1)$ from the return probability and define the fidelity density as $\log P(T_1)/N$. The weak dependence on $N$ indicates that the revival weight does not exhibit strong exponential suppression within the accessible system sizes.
• Figure 5: Fourier power spectra $|F(\Delta E)|^2$ of the fidelity $P(t)$. The Fourier spectrum of $P(t)$ is calculated for three distinct time intervals. The three spectra almost perfectly overlap, displaying a series of evenly spaced peaks, although the spectral amplitude gradually decreases. Each spectrum is normalized by its maximum value. The particle number is $N=40$ and the interactions are $c_0=1.0$ and $c_2=0.1$.