Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Dynamical Effects

TL;DR

This paper investigates how dynamical effects influence matrix element fluctuations in ballistic quantum dots, revealing significant deviations from random wave model predictions and implications for quantum dot spectral properties.

Contribution

It demonstrates that actual chaotic billiards exhibit larger matrix element fluctuations than predicted by the random wave model due to dynamical effects.

Findings

Matrix element variances are 3-4 times larger than model predictions.

Covariance signs differ from random wave model predictions.

Enhanced fluctuations impact spectral statistics in quantum dots.

Abstract

We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots, comparing behavior in actual chaotic billiards with analytic results previously obtained in a normalized random wave model. We find that the matrix element variances in actual chaotic billiards typically exceed by a factor of 3 or 4 the predictions of the random wave model, for dot sizes commonly used in experiments. We discuss dynamical effects that are responsible for this enhancement. These dynamical effects have an even more striking effect on the covariance, which changes sign when compared with random wave predictions. In billiards that do not display hard chaos, an even larger enhancement of matrix element fluctuations is possible. These enhanced fluctuations have implications for peak spacing statistics and spectral scrambling for quantum dots in the Coulomb blockade regime.