Conductance-phase determination in double-slit transmission across a quantum dot using a Hilbert transform method

Recent mesoscopic two-arm experiments involving quantum dots, electron interferometry, and Aharonov-Bohm effects have enabled measurements of both electron transmission probabilities and phases. Unexpected features in the phases as function of the gap voltage U have stimulated several theoretical works. It is shown in this paper that the phases (f ) and conductances (|C|), appearing both in the experimental and in theoretical studies, are interrelated through integral expressions, causing f and $\ln \left(|C|\right)$ to be Hilbert transforms. The empirically found interrelations imply certain analytical properties of the U dependence of wave functions in mesoscopic systems.