  The regimes of growing phases (for electron numbers N~0-8) that pass into
regions of self-returning phases (for N>8), found recently in quantum dot
conductances by the Weizmann group are accounted for by an elementary Green
function formalism, appropriate to an equi-spaced ladder structure (with at
least three rungs) of electronic levels in the quantum dot. The key features of
the theory are physically a dissipation rate that increases linearly with the
level number (and tentatively linked to coupling to longitudinal optical
phonons) and a set of Fano-like meta-stable levels, which disturb the
unitarity, and mathematically the change over of the position of the complex
transmission amplitude-zeros from the upper-half in the complex gap-voltage
plane to the lower half of that plane. The two regimes are identified with
(respectively) the Blaschke-term and the Kramers-Kronig integral term in the
theory of complex variables.
