Distribution of parametric conductance derivatives of a quantum dot

TL;DR

This paper derives the statistical distribution of conductance and its derivatives in a quantum dot, revealing singularities, correlations, and effects of Coulomb interactions, with implications for experiments in microstructures and microwave cavities.

Contribution

It introduces a novel analytical framework relating conductance derivatives to the Wigner-Smith time-delay matrix in chaotic quantum dots, including Coulomb interaction effects.

Findings

Distribution of dG/dX has a singularity at zero

Ratio of dG/dX to sqrt(G(1-G)) is independent of G

Coulomb interactions induce a transition from grand-canonical to canonical ensemble

Abstract

The conductance G of a quantum dot with single-mode ballistic point contacts depends sensitively on external parameters X, such as gate voltage and magnetic field. We calculate the joint distribution of G and dG/dX by relating it to the distribution of the Wigner-Smith time-delay matrix of a chaotic system. The distribution of dG/dX has a singularity at zero and algebraic tails. While G and dG/dX are correlated, the ratio of dG/dX and $\sqrt{G(1-G)}$ is independent of G. Coulomb interactions change the distribution of dG/dX, by inducing a transition from the grand-canonical to the canonical ensemble. All these predictions can be tested in semiconductor microstructures or microwave cavities.