  The properties of scattering phases in quantum dots are analyzed with the
help of lattice models. We first derive the expressions relating the different
scattering phases and the dot Green functions. We analyze in detail the Friedel
sum rule and discuss the deviation of the phase of the transmission amplitude
from the Friedel phase at the zeroes of the transmission. The occurrence of
such zeroes is related to the parity of the isolated dot levels. A statistical
analysis of the isolated dot wave-functions reveals the absence of significant
correlations in the parity for large disorder and the appearance, for weak
disorder, of certain dot states which are strongly coupled to the leads. It is
shown that large differences in the coupling to the leads give rise to an
anomalous charging of the dot levels. A mechanism for the phase lapse observed
experimentally based on this property is discussed and illustrated with model
calculations.
