  The dynamics of a many-body system can take many forms, from a purely
reversible evolution to fast thermalization. Here we show experimentally and
numerically that an assembly of spin 1 atoms all in the same spatial mode
allows one to explore this wide variety of behaviors. When the system can be
described by a Bogoliubov analysis, the relevant energy spectrum is linear and
leads to undamped oscillations of many-body observables. Outside this regime,
the non-linearity of the spectrum leads to irreversibity, characterized by a
universal behavior. When the integrability of the Hamiltonian is broken, a
chaotic dynamics emerges and leads to thermalization, in agreement with the
Eigenstate Thermalization Hypothesis paradigm.
