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The regimes of growing phases (for electron numbers N~0-8) that pass intoregions of self-returning phases (for N>8), found recently in quantum dotconductances by the Weizmann group are accounted for by an elementary Greenfunction formalism, appropriate to an equi-spaced ladder structure (with atleast three rungs) of electronic levels in the quantum dot. The key features ofthe theory are physically a dissipation rate that increases linearly with thelevel number (and tentatively linked to coupling to longitudinal opticalphonons) and a set of Fano-like meta-stable levels, which disturb theunitarity, and mathematically the change over of the position of the complextransmission amplitude-zeros from the upper-half in the complex gap-voltageplane to the lower half of that plane. The two regimes are identified with(respectively) the Blaschke-term and the Kramers-Kronig integral term in thetheory of complex variables.Comment: 20 pages, 4 figure

Conductance phases in the quantum dots of an Aharonov-Bohm ring