  We study the transmission through different small systems as a function of
the coupling strength $v$ to the two attached leads. The leads are identical
with only one propagating mode $\xi^E_C$ in each of them. Besides the
conductance $G$, we calculate the phase rigidity $\rho$ of the scattering wave
function $\Psi^E_C$ in the interior of the system. Most interesting results are
obtained in the regime of strongly overlapping resonance states where the
crossover from staying to traveling modes takes place. The crossover is
characterized by collective effects. Here, the conductance is plateau-like
enhanced in some energy regions of finite length while corridors with zero
transmission (total reflection) appear in other energy regions. This
transmission picture depends only weakly on the spectrum of the closed system.
It is caused by the alignment of some resonance states of the system with the
propagating modes $\xi^E_C$ in the leads. The alignment of resonance states
takes place stepwise by resonance trapping, i.e. it is accompanied by the
decoupling of other resonance states from the continuum of propagating modes.
This process is quantitatively described by the phase rigidity $\rho$ of the
scattering wave function. Averaged over energy in the considered energy window,
$<G>$ is correlated with $1-<\rho>$. In the regime of strong coupling, only two
short-lived resonance states survive each aligned with one of the channel wave
functions $\xi^E_C$. They may be identified with traveling modes through the
system. The remaining $M-2$ trapped narrow resonance states are well separated
from one another.
