  We show that the observed evolution of the transmission phase through
multi-electron quantum dots with more than approximately ten electrons, which
shows a universal (i.e., independent of N) as yet unexplained behavior, is
consistent with an electrostatic model, where electron-electron interaction is
described by a mean-field approach. Moreover, we perform exact calculations for
an open 1D quantum dot and show that carrier correlations may give rise to a
non-universal (i.e., N-dependent) behavior of the transmission phase, ensuing
from Fano resonances, which is consistent with experiments with a few (N < 10)
carriers. Our results suggest that in the universal regime the coherent
transmission takes place through a single level while in the few-particle
regime the correlated scattering state is determined by the number of bound
particles.
