  We study the non-equiliribium dynamics of atom-molecule Bose gases in a
double-well potential. In this system, the internal atom-molecule tunneling has
significant influence on the dynamics. We investigate the periodicity of
dynamics by studying the level statistics of the quantum system. We find that
chaotic energy eigenstates arise from the competition between the interwell and
the atom-molecule internal tunnelings. Furthermore, we show that the physical
quantities relax to the microcanonical averages in the full-quantum dynamics
when the system is chaotic. This thermalization is caused by the verification
of eigenstate thermalization hypothesis (ETH). We show numerically that the
onset of ETH occurs simultaneously with that of chaos. In addition, we show
that the energy eigenstates become to be exponentially localized states
simultaneously with the onset of chaos.

Quantum Gases;Quantum Physics