Strong Eigenstate Thermalization from Mean-Ergodic Non-chaotic Dynamics

Abstract

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 \textit{strong} eigenstate thermalization hypothesis (ETH) in the quantum regime. The analysis addresses a key open question: whether \textit{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 $D^{-1/2}$, where $D$ denotes the Hilbert space dimension. Furthermore, the off-diagonal matrix elements show parameter-independent distribution, together with a smooth function $f_O(\bar{E},\ddot{I}‰)$ that becomes nearly uniform in the large-$k_{\hat{I}}¸$ domain. Our findings show that even mean-ergodic and non-chaotic systems can exhibit \textit{strong} ETH.

5 pages (two-column) + 5 pages (one-column) + 12 figures. Few figures are corrected. Comments are welcome