Key points are not available for this paper at this time.
It is shown (by means of a perturbation series) that for a class of potentials V (x) the stationary distribution of the solution x (t) of the quantum Langevin equation approaches in the weak-coupling limit (f0) the quantum mechanical canonical distribution of the displacement of the oscillator, subject to the potential V (x), if and only if E (t) is the operator version of the purely random Gaussian process so that, in particular, higher symmetrized averages 〈E ({t₁) (t₍) 〉}ₒ are expressible in terms of pair correlations, in the usual way.
Benguria et al. (Mon,) studied this question.