Strong Eigenstate Thermalization from Mean-Ergodic Non-chaotic Dynamics

We report an example of a many-body system, derived from the double kicked top (DKT), with non-chaotic yet mean-ergodic dynamics that displays $\mathit{\text{strong}}$ eigenstate thermalization hypothesis (ETH) in the quantum regime. The analysis addresses a key open question: whether $\mathit{\text{strong}}$ ETH is a quantum analog of ergodicity (or mean-ergodicity). Despite non-chaotic dynamics, the fluctuations of the diagonal matrix elements of an observable scale as $D^{-1\mathrm{/}2}$, where $D$ denotes the Hilbert space dimension. Furthermore, the off-diagonal matrix elements show parameter-independent distribution, together with a smooth function $f_O(\bar{E},\omega )$ that becomes nearly uniform in the large-$k_{\theta }$ domain. Our findings show that even mean-ergodic and non-chaotic systems can exhibit $\mathit{\text{strong}}$ ETH.