The regimes of growing phases (for electron numbers $N\approx 0–8$) that pass into regions of self-returning phases (for $N>8$), found recently in quantum dot conductances by Heiblum and co-workers are accounted for by an elementary Green’s 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 is tentatively linked to coupling to longitudinal optical phonons) and a set of Fano-like metastable levels, which disturb the unitarity, and mathematically the changeover 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.

• Received 13 November 2005

DOI:https://doi.org/10.1103/PhysRevB.74.115328