Interaction matrix element fluctuations in quantum dots

TL;DR

This paper investigates fluctuations of interaction matrix elements in quantum dots, showing that realistic geometries exhibit larger fluctuations than random wave models predict, which could improve agreement with experimental conductance data.

Contribution

The study provides analytic expressions for matrix element fluctuations in realistic chaotic geometries, highlighting their larger magnitude and non-Gaussian distribution compared to random wave models.

Findings

Fluctuations exceed random wave model predictions by a factor of 3-4 in realistic geometries.

Distribution of matrix elements is strongly non-Gaussian.

Enhanced fluctuations are linked to short-time dynamics beyond semiclassical approximation.

Abstract

In the Coulomb blockade regime of a ballistic quantum dot, the distribution of conductance peak spacings is well known to be incorrectly predicted by a single-particle picture; instead, matrix element fluctuations of the residual electronic interaction need to be taken into account. In the normalized random-wave model, valid in the semiclassical limit where the number of electrons in the dot becomes large, we obtain analytic expressions for the fluctuations of two-body and one-body matrix elements. However, these fluctuations may be too small to explain low-temperature experimental data. We have examined matrix element fluctuations in realistic chaotic geometries, and shown that at energies of experimental interest these fluctuations generically exceed by a factor of about 3-4 the predictions of the random wave model. Even larger fluctuations occur in geometries with a mixed chaotic-regular phase space. These results may allow for much better agreement between the Hartree-Fock picture and experiment. Among other findings, we show that the distribution of interaction matrix elements is strongly non-Gaussian in the parameter range of experimental interest, even in the random wave model. We also find that the enhanced fluctuations in realistic geometries cannot be computed using a leading-order semiclassical approach, but may be understood in terms of short-time dynamics.