  The collective and purely relaxational dynamics of quantum many-body systems
after a quench at temperature $T=0$, from a disordered state to various phases
is studied through the exact solution of the quantum Langevin equation of the
spherical and the $O(n)$-model in the limit $n\to\infty$. The stationary state
of the quantum dynamics is shown to be a non-equilibrium state. The quantum
spherical and the quantum $O(n)$-model for $n\to\infty$ are in the same
dynamical universality class. The long-time behaviour of single-time and
two-time correlation and response functions is analysed and the universal
exponents which characterise quantum coarsening and quantum ageing are derived.
The importance of the non-Markovian long-time memory of the quantum noise is
elucidated by comparing it with an effective Markovian noise having the same
scaling behaviour and with the case of non-equilibrium classical dynamics.
