The regimes of growing phases (for electron numbers N ≈ 1 − 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 of bound electronic levels in the quantum well and resonant states above it. The key features of the theory are physically a dissipation rate that increases linearly with the level number (and tentatively linked to a coupling to longitudinal optical (LO) phonons) 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. PACS numbers: 03.65.V
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