Absence of thermal smearing for the transmission phase through a quantum dot

We derive the phase theta of the Aharonov-Bohm oscillations of a multi-terminal electron ring with a quantum dot in one of its arms. We show i) that theta varies smoothly by pi at each transmission peak of the system. We also find ii) that theta drops sharply by pi between the peaks if consecutive peaks have similar resonance parameters. The characteristic energy scale for ii) is of the order of the intrinsic resonance width Gamma. This fact can be employed to measure Gamma in a novel way.