Broken Unitarity and Phase Measurements in Aharonov-Bohm Interferometers

Aharonov-Bohm mesoscopic solid-state interferometers yield a conductance which contains a term cos(φ+β), where φ relates to the magnetic flux. Experiments with a quantum dot on one of the interfering paths aim to relate β to the dot's intrinsic Friedel transmission phase α₁. For closed systems, which conserve the electron current (unitarity), the Onsager relation requires that β0ex0ex=0ex0ex0 or π. For open systems, we show that in general β depends on the details of the broken unitarity. Although it gives information on the resonances of the dot, β is generally not equal to α₁. A direct relation between β and α₁ requires specific ways of opening the system, which are discussed.