Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Random Wave Model

TL;DR

This paper analyzes fluctuations of matrix elements in ballistic quantum dots using a random wave model, revealing non-Gaussian distributions and providing analytical and numerical insights into their variances and covariances.

Contribution

It introduces an analytical framework for matrix element fluctuations in chaotic quantum dots, highlighting non-Gaussian behavior and comparing with numerical results.

Findings

Matrix elements follow strongly non-Gaussian distributions.

Analytical expansions for variances and covariances are derived.

Numerical results confirm the analytical predictions.

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. For chaotic dots, we use a normalized random wave model to obtain analytic expansions for matrix element variances and covariances in the limit of large kL (where k is the Fermi wave number and L the linear size of the dot). These leading-order analytical results are compared with exact numerical results. Both two-body and one-body matrix elements are shown to follow strongly non-Gaussian distributions, despite the Gaussian random nature of the single-electron wave functions.