  Time evolution of a harmonic oscillator linearly coupled to a heat bath is
compared for three classes of initial states for the bath modes - grand
canonical ensemble, number states and coherent states. It is shown that for a
wide class of number states the behavior of the oscillator is similar to the
case of the equilibrium bath. If the bath modes are initially in coherent
states, then the variances of the oscillator coordinate and momentum, as well
as its entanglement to the bath, asymptotically approach the same values as for
the oscillator at zero temperature and the average coordinate and momentum show
a Brownian-like behavior. We derive an exact master equation for the
characteristic function of the oscillator valid for arbitrary factorized
initial conditions. In the case of the equilibrium bath this equation reduces
to an equation of the Hu-Paz-Zhang type, while for the coherent states bath it
leads to an exact stochastic master equation with a multiplicative noise.
