Variational treatment of a harmonic oscillator coupled to a dissipative heat bath

摘要

We consider the problem of a single quantum oscillator coupled linearly to a heat bath of independent harmonic modes. An exact solution is presented for the systemhyphen;oscillator observables of interest. The exact results are then used to evaluate the utility of a variational approach to the problem that has proven useful recently in elucidating the dynamics of dissipatively coupled systems. We find that the variational approach does provide a good description for most, but not all, observables of interest. Both the exact and the variational treatment demonstrate the important role played by the lowhyphen;frequency bath modes in determining qualitative features of the dynamical behavior.