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 inte rferometry, and Aharonov-Bohm effects have enabled measurements of both ele ctron transmission probabilities and phases. Unexpected features in the pha ses as function of the gap voltage U have stimulated several theoretical wo rks. It is shown in this paper that the phases (f) and conductances (\C\), appearing both in the experimental and in theoretical studies, are interrel ated through integral expressions, causing f and In(\C\) to be Hilbert tran sforms. The empirically found interrelations imply certain analytical prope rties of the U dependence of wave functions in mesoscopic systems.