  Quantum mechanically, a driving process is expected to be reversible in the
quasistatic limit, also known as the adiabatic theorem. This statement stands
in opposition to classical mechanics, where a mix of regular and chaotic
dynamics implies irreversibility. A paradigm for demonstrating the signatures
of chaos in quantum irreversibility is a sweep process whose objective is to
transfer condensed bosons from a source orbital. We show that such a protocol
is dominated by an interplay of adiabatic-shuttling and chaos-assisted
depletion processes. The latter is implied by interaction terms that spoil the
Bogoliubov integrability of the Hamiltonian. As the sweep rate is lowered, a
crossover to a regime that is dominated by quantum fluctuations is encountered,
featuring a breakdown of quantum-to-classical correspondence. The major aspects
of this picture are not captured by the common two-orbital approximation, which
implies failure of the familiar many-body Landau-Zener paradigm.
