Universal Parametric Correlations of Conductance Peaks in Quantum Dots

TL;DR

This paper derives a universal parametric correlation function for conductance peaks in quantum dots, showing its independence from lead details and dependence on eigenfunctions, with validation through simulations.

Contribution

It introduces a new scaling for conductance peak correlations that depends solely on eigenfunctions, enhancing understanding of universality in quantum dot conductance behavior.

Findings

Correlation function affected by time-reversal symmetry breaking

Correlation function independent of lead channel details

Derived scaling depends only on eigenfunctions

Abstract

We compute the parametric correlation function of the conductance peaks in chaotic and weakly disordered quantum dots in the Coulomb blockade regime and demonstrate its universality upon an appropriate scaling of the parameter. For a symmetric dot we show that this correlation function is affected by breaking time-reversal symmetry but is independent of the details of the channels in the external leads. We derive a new scaling which depends on the eigenfunctions alone and can be extracted directly from the conductance peak heights. Our results are in excellent agreement with model simulations of a disordered quantum dot.