Internal Decoherence of a Gaussian Wave Packet in a Harmonic Potential

We have studied the quantum dissipative problem of a Gaussian wave packet under the influence of a harmonic potential. A phenomenological approach to dissipation is adopted in the light of the well-known model in which the environment is composed of a bath of non-interacting harmonic oscillators. As one of the effects of the coupling to the bath is the evolution of an initially pure wave packet into a statistical mixture, we estimate the characteristic time elapsed for this to occur for different regimes of temperature, damping, and also different initial states.