S_{\mathrm{dr}} [ {\omega}_{1},{\omega}_{2}]$ has a different frequency dependence in the quantum limit (${\bar n}_{ \rm{th} }=0$) from its classical limit ${\tilde S}_{ \mathrm{cl}}[ {\omega}_{1},{\omega}_{2}]$. To see this, it is useful to write $$\frac{S_{\mathrm{dr}} [ {\omega}_{1},{\omega}_{2}] }{{\bar n}_{ \rm{dr} }}
     =   ( 2{\bar n}_{ \rm{th} }+1)^2 \!  {\tilde S}_{ \mathrm{cl}}[ {\omega}_{1},{\omega}_{2}] 
     + 
      {\tilde S}_{ \mathrm{q}}[ {\omega}_{1},{\omega}_{2}]  .$$ The first term is the classical contribution which dominates in the high-temperature limit; ${\tilde S}_{ \mathrm{cl}}[ {\omega}_{1},{\omega}_{2}]$ is independent of both $ {\bar n}_{ \rm{dr} } ,{\bar n}_{ \rm{th} }$, and is real and positive for all frequencies. Its form can be found directly from a classical Langevin equation calculation (see Eq.  of the SM [@SI]). In contrast, the second term is the temperature-independent quantum correction. It has a [*completely different*]{} frequency dependence from the classical limit, as described by ${\tilde S}_{ \mathrm{q}}[ {\omega}_{1},{\omega}_{2}]$ $${\tilde S}_{ \mathrm{q}}[ {\omega}_{1},{\omega}_{2}] = -\frac{1}{2 } \! \! \sum\limits_{ \substack{\alpha  \ne \beta \\ \alpha ,\beta  = 1,2,3  }}   \frac{\frac{\gamma }{2} + i{ \omega} _\beta }{ (\gamma  - i { \omega} _\alpha) [( \frac{\gamma }{2} + i { \omega}_\beta  )^2+ \delta ^2]}.
 \label{eq:Sdr2qu}$$ This function can have both a negative real part, and a non-zero imaginary part. In the quantum 