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Recent novel mesoscopic two-arm experiments involving quantum dots, electroninterferometry and Aharononov-Bohm effects have enabled measuring the electrontransmission probabilities and the phases. Unexpected features in the phases asfunction of the gap voltage U have simulated intensive theoretical works. It isshown in this paper that the phases (f) and conductances (|C|), appearing inboth the experimental and the theoretical works, are interrelated throughintegral expressions, causing f and log(|C|) to be Hilbert transforms. Theempirically found interrelations imply remarkable analytical properties of theU-dependence of wave-functions in mesoscopic systems

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