  The dynamics of a weakly interacting Bose gas at low temperatures is close to
integrable due to the approximate quadratic nature of the many-body
Hamiltonian. While the short-time physics after an abrupt ramp of the
interaction constant is dominated by the integrable dynamics, integrability is
broken at longer times by higher-order interaction terms in the Bogoliubov
Hamiltonian, in particular by Beliaev-Landau scatterings involving three
quasiparticles. The two-stage relaxation process is highlighted in the
evolution of local observables such as the density-density correlation
function: a dephasing mechanism leads the system to a prethermal stage,
followed by true thermalization conveyed by quasiparticle collisions. Our
results bring the crossover from prethermalization to thermalization within
reach of current experiments with ultracold atomic gases.
