  The dynamics of a typical open quantum system, namely a quantum Brownian
particle in a harmonic potential, is studied focussing on its non-Markovian
regime. Both an analytic approach and a stochastic wave function approach are
used to describe the exact time evolution of the system. The border between two
very different dynamical regimes, the Lindblad and non-Lindblad regimes, is
identified and the relevant physical variables governing the passage from one
regime to the other are singled out. The non-Markovian short time dynamics is
studied in detail by looking at the mean energy, the squeezing, the Mandel
parameter and the Wigner function of the system.
