Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots

TL;DR

This paper demonstrates that the correlations of conductance peak amplitudes in chaotic quantum dots become universal when scaled appropriately, introducing a new rotation scaling derived from eigenfunction rotation rates.

Contribution

It introduces the rotation scaling, a novel method to achieve universality in conductance peak correlations without requiring spectral information.

Findings

Universal conductance peak correlator forms are derived for different symmetry classes.

The rotation scaling can be computed from eigenfunction rotation rates or conductance peak heights.

Universal distributions of level width velocity are calculated for various scaled parameters.

Abstract

We show that the parametric correlations of the conductance peak amplitudes of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime become universal upon an appropriate scaling of the parameter. We compute the universal forms of this correlator for both cases of conserved and broken time reversal symmetry. For a symmetric dot the correlator is independent of the details in each lead such as the number of channels and their correlation. We derive a new scaling, which we call the rotation scaling, that can be computed directly from the dot's eigenfunction rotation rate or alternatively from the conductance peak heights, and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the universal distributions of the average level width velocity for various values of the scaled parameter. The universality is illustrated in an Anderson model of a disordered dot.