  We study the particle-entanglement dynamics witnessed by the quantum Fisher
information (QFI) of a trapped Bose-Einstein condensate governed by the kicked
rotor Hamiltonian. The dynamics is investigated with a beyond mean-field
approach. We link the time scales of the validity of this approximation in,
both, classical regular and chaotic regions, with the maximum Lyapunov
exponents of the classical system. This establishes an effective connection
between the classical chaos and the QFI. We finally study the critical point of
a quantum phase transition using the beyond mean-field approximation by
considering a two-mode bosonic Josephson junction with attractive interparticle
interaction.
