The initial condition problem of damped quantum harmonic oscillator

We investigate the exact dynamics of the damped quantum harmonic oscillator under the (un)correlated initial conditions. We generalize the master equation to the cases of arbitrary factorized state and/or Gaussian state. For the factorized Gaussian state, we demonstrate that the effects of the initial oscillator-bath correlation are unnoticeable for the evolutions of variances, but can become remarkable for the evolutions of mean values even at high temperature. We also show that the initial dip during the purity evolution always shows up for the factorized initial state, but can disappear for some correlated non-factorizable initial state. Finally, we study the effects of repeated measurements on the time evolution of the damped oscillator. The comparison with the weak coupling results indicates that even for an intermediate coupling, they can give quite different transient behaviors.