Statistics of Transmission Eigenvalues for a Disordered Quantum Point Contact

TL;DR

This paper analyzes the distribution of transmission eigenvalues in a disordered quantum point contact, revealing how it depends on the number of channels and reflection properties, with results bridging Poissonian and circuit theory regimes.

Contribution

It introduces a model connecting Gaussian random reflection matrices to transmission eigenvalue distributions in disordered quantum point contacts.

Findings

Distribution depends on number of open channels and average reflection eigenvalue.

Crosses over from Poissonian to circuit theory distribution as channels increase.

Provides a unified framework for understanding transmission in disordered systems.

Abstract

We study the distribution of transmission eigenvalues of a quantum point contact with nearby impurities. In the semi-classical case (the chemical potential lies at the conductance plateau) we find that the transmission properties of this system are obtained from the ensemble of Gaussian random reflection matrices. The distribution only depends on the number of open transport channels and the average reflection eigenvalue and crosses over from the Poissonian for one open channel to the form predicted by the circuit theory in the limit of large number of open channels.