Chaos and thermalization in a trapped boson system I: thermal states

A detailed study of chaos and thermalization is performed for a system of bosonic atoms trapped in a linear chain with disorder. For large values of the disorder parameter, the system is regular and localized. For weak disorder, the presence of chaos and the validity of the Eigenstate Thermalization Hypothesis are exhibited for most eigenstates, while those in the extrema of the energy spectrum are regular and do not thermalize. We study the temporal evolution of the experimentally accessible states of the occupation basis. The whole set of states of this basis are classified according to their maximum occupation and a crowding parameter, which has a linear relation with their average energy. Those states whose energies lie in the chaotic region have larger participation ratios in the eigenbasis, while those in the regular region have participation ratios noticeably smaller. The states with the largest participation ratio in the chaotic region exhibit the characteristic random matrix correlation hole in their survival probability, while those in the regular region do not, and have revivals for a long time.