Transmission phase alpha measurements of many-electron quantum dots (small mean level spacing delta) revealed universal phase lapses by pi between consecutive resonances. In contrast, for dots with only a few electrons (large delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multi-level quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of alpha for small delta follows from Fano-type antiresonances of the renormalized single-particle levels.
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