Not yet reviewed by Pith; the record is open.

The low energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos manifests itself in these systems. In this paper, we consider a simple but experimentally relevant one-dimensional system of a few ultracold fermions moving in a double-well potential. We analyze its many-body spectral properties, which are commonly used to trace quantum chaos. We observe some signatures of quantum chaos already in the system with three particles. Generally, these signatures become more pronounced when fermions are evenly added to both components. On the contrary, they become suppressed when the particle imbalance is increased.