Broken Unitarity and Phase Measurements in Aharonov-Bohm Interferometers

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