  The application of quantum Langevin equations for the study of
non-equilibrium relaxations is illustrated in the exactly solved quantum
spherical model. Tutorial sections on the physical background of non-markovian
quantum noise, the spherical model quantum phase transition, the long-time
limit of the quantum Langevin equation of the spherical model and physical
ageing are followed by a brief review of the solution of the non-markovian
time-dependent spherical constraint and about the consequences for quantum
ageing at zero temperature, after a quantum quench.
