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 In(\C\) to be Hilbert transforms. The empirically found interrelations imply certain analytical properties of the U dependence of wave functions in mesoscopic systems.