Independent-Electron Model for the Phase of the Transmission Amplitude in Quantum Dots

Motivated by a recent experiment by Yacoby et al.\ [preprint, 1994], we calculate magnitude and phase $\alpha$ of the transmission amplitude through a quantum dot. We work in the Coulomb blockade regime, assume the electrons not to interact, and consider tunneling through isolated resonances. Assuming a non--resonant background, we find that $\alpha$ increases by $2 \pi$ over each resonance, with a sharp rise by $\pi$ over an energy interval much smaller than the thermal width. This is consistent with the experimental data. Our assumptions can be tested by further experiments.