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 ($f\ensuremath{\rightarrow}0$) 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 ${〈E({t}_{1})\ensuremath{\cdots}E({t}_{n})〉}_{s}$ are expressible in terms of pair correlations, in the usual way.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 ($f\ensuremath{\rightarrow}0$) 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 ${〈E({t}_{1})\ensuremath{\cdots}E({t}_{n})〉}_{s}$ are expressible in terms of pair correlations, in the usual way.

Physical Review LettersJan 5, 1981305 citations

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 ($f\ensuremath{\rightarrow}0$) 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 ${〈E({t}_{1})\ensuremath{\cdots}E({t}_{n})〉}_{s}$ are expressible in terms of pair correlations, in the usual way.