  The conventional conception of decoherence relies on the interaction with an
external set of degrees of freedom - the 'bath' - to which the system loses
quantum information. But the role of the bath can be played too by any internal
degrees of freedom that are not accessible to the observer, and in this sense
we can talk about 'Self-Induced Decoherence'. Simulating the exact
time-evolution of the few-body Bose-Hubbard Hamiltonian, we provide numerical
evidence of the decay of quantum purity in the sense of 'temporal typicality'
referred in the context of pure state Quantum Statistical Mechanics. We analyse
the causes of such purity loss in terms of the structural differences of the
interacting many-body Hamiltonian in comparison with its non-interacting
counterpart, finding that the predominant role in the long term behaviour is
played by the shifts in the many-body energy spectrum.
