Parametric correlation of Coulomb blockade conductance peaks in chaotic quantum dots

TL;DR

This paper studies how conductance peak heights in chaotic quantum dots are correlated, using Random Matrix Theory and numerical models, revealing universal behavior dependent on symmetry and lead channels.

Contribution

It provides a parametric correlation function for conductance peaks in Coulomb blockade quantum dots, incorporating symmetry and channel effects with analytical, numerical, and semiclassical methods.

Findings

Correlator becomes universal after rescaling.

Correlation depends on symmetry and number of channels.

Semiclassical estimate of the scaling parameter.

Abstract

We investigate the autocorrelator of conductance peak heights for quantum dots in the Coulomb blockade regime. Analytical and numerical results based on Random Matrix Theory are presented and compared to exact numerical calculations based on a simple dynamical model. We consider the case of preserved time-reversal symmetry, which is realized experimentally by varying the shape of the quantum dot in the absence of magnetic fields. Upon a proper rescaling, the correlator becomes independent of the details of the system and its form is solely determined by symmetry properties and the number of channels in the leads. The magnitude of the scaling parameter is estimated by a semiclassical approach.