Conductance-Phase Determination in Double Slit Transmission across a Quantum Dot by Hilbert Transform Method

TL;DR

This paper reveals that in mesoscopic quantum dot experiments, the conductance and phase are mathematically interconnected through Hilbert transforms, providing new insights into their U-dependent behavior.

Contribution

It introduces a Hilbert transform-based method to relate conductance and phase in quantum dot transmission, highlighting their analytical interdependence.

Findings

Conductance and phase are linked via Hilbert transforms.

The U-dependence of wave-functions exhibits remarkable analytical properties.

Experimental and theoretical data support the Hilbert transform relationship.

Abstract

Recent novel mesoscopic two-arm experiments involving quantum dots, electron interferometry and Aharononov-Bohm effects have enabled measuring the electron transmission probabilities and the phases. Unexpected features in the phases as function of the gap voltage U have simulated intensive theoretical works. It is shown in this paper that the phases (f) and conductances (|C|), appearing in both the experimental and the theoretical works, are interrelated through integral expressions, causing f and log(|C|) to be Hilbert transforms. The empirically found interrelations imply remarkable analytical properties of the U-dependence of wave-functions in mesoscopic systems.