Two simple systems with cold atoms: quantum chaos tests and non-equilibrium dynamics

This paper is an attempt to establish a link between the quantum nonequilibrium dynamics of cold gases and 50 years of progress in low-dimensional quantum chaos. We identify two atomic systems lying in the interface: two interacting atoms in a harmonic multimode waveguide and an interacting two-component Bose-Bose mixture in a double-well potential. In particular, we study the level spacing distribution, the wavefunction statistics, the eigenstate thermalization and the ability to thermalize in a relaxation process as such.