  The equation for the Wigner function describing the reduced dynamics of a
single harmonic oscillator, coupled to an oscillator bath, was obtained by
Karrlein and Grabert [Phys. Rev. E, vol. 55, 153 (1997)]. It was shown that for
some special correlated initial conditions the equation reduces, in the
classical limit, to the corresponding classical Fokker-Planck equation obtained
by Adelman [J. Chem Phys., vol. 64, 124 (1976)]. However for separable initial
conditions the Adelman equations were not recovered. We resolve this problem by
showing that, for separable initial conditions, the classical Langevin equation
obtained from the oscillator bath model is somewhat different from the one
considered by Adelman. We obtain the corresponding Fokker-Planck equation and
show that it exactly matches the classical limit of the equation for the Wigner
function obtained from the master equation for separable initial conditions. We
also discuss why the special correlated initial conditions correspond to
Adelman's solution.
