  The parametric correlations of the transmission eigenvalues $T_i$ of a
$N$-channel quantum scatterer are calculated assuming two different Brownian
motion ensembles. The first one is the original ensemble introduced by Dyson
and assumes an isotropic diffusion for the $S$-matrix. The second Brownian
motion ensemble assumes for the transfer matrix $M$ an isotropic diffusion
yielded by a multiplicative combination law. We review the qualitative
differences between transmission through two weakly coupled quantum dots and
through a disordered line and we discuss the mathematical analogies between the
Fokker-Planck equations of the two Brownian motion models.
