The Statistical Distributions of Level Widths and Conductance Peaks in Irregularly Shaped Quantum Dots

TL;DR

This paper derives analytical expressions for the distributions of level widths and conductance peaks in irregular quantum dots, accounting for multiple channels and symmetry conditions, and validates predictions with numerical simulations.

Contribution

It provides the first comprehensive analytical framework for width and conductance peak distributions in multi-channel quantum dots with arbitrary channel correlations and symmetry considerations.

Findings

Distributions expressed in terms of channel correlation matrix M.

Closed-form expression for matrix M.

Numerical validation using a chaotic billiard model.

Abstract

Analytical expressions for width and conductance peak distributions for quantum dots with multi-channel leads in the Coulomb blockade regime are presented for both limits of conserved and broken time-reversal symmetry. The results are valid for any number of non-equivalent and correlated channels, and the distributions are expressed in terms of the channel correlation matrix $M$ in each lead. The matrix $M$ is also given in closed form. A chaotic billiard is used as a model to test numerically the theoretical predictions.