  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.
