Emergence of correlations in the process of thermalization of interacting bosons

The relevance of thermalization to the increase of correlations in the quench dynamics of an isolated system with a finite number of interacting bosons has been studied. Specifically, we analyze how correlations between occupation numbers increase in time resulting in the emergence of the Bose-Einstein distribution. Before saturation, the two-point correlation function increases quadratically in time (as predicted by perturbation theory), while the out-of-time-order correlator (OTOC) increases algebraically with an exponent 2.5 beyond the perturbative region. Our results, that can be confirmed experimentally in traps with interacting bosons, may be also relevant to the problem of black hole scrambling.