  The many-body Schr\"odinger dynamics of a one-dimensional bosonic Josephson
junction is investigated for up to ten thousand bosons and long times. The
initial states are fully condensed and the interaction strength is weak. We
report on a universal fragmentation dynamics on the many-body level: systems
consisting of different numbers of particles fragment to the same value at
constant mean-field interaction strength. The phenomenon manifests itself in
observables such as the correlation functions of the system. We explain this
universal fragmentation dynamics analytically based on the Bose-Hubbard model.
We thereby show that the extent to which many-body effects become important at
later times depends crucially on the initial state. Even for arbitrarily large
particle numbers and arbitrarily weak interaction strength the dynamics is
many-body in nature and the fragmentation universal. There is no weakly
interacting limit where the Gross-Piatevskii mean-field is valid for long
times.
