Towards a semiclassical justification of the `effective random matrix theory' for transport through ballistic chaotic quantum dots

TL;DR

This paper investigates the validity of the effective random matrix theory for quantum transport in ballistic chaotic quantum dots by comparing its predictions with semiclassical calculations, focusing on leading-order behavior in the number of channels.

Contribution

It provides a partial verification of the effective random matrix theory's accuracy for ensemble averages of polynomial functions of the scattering matrix at leading order.

Findings

Effective random matrix theory matches semiclassical results for certain polynomial averages.

Theory correctly describes leading-order quantum transport in chaotic quantum dots.

Partial verification supports the use of the theory for transport predictions.

Abstract

The scattering matrix S of a ballistic chaotic cavity is the direct sum of a `classical' and a `quantum' part, which describe the scattering of channels with typical dwell time smaller and larger than the Ehrenfest time, respectively. According to the `effective random matrix theory' of Silvestrov, Goorden, and Beenakker [Phys. Rev. Lett. 90, 116801 (2003)], statistical averages involving the quantum-mechanical scattering matrix are given by random matrix theory. While this effective random matrix theory is known not to be applicable for quantum interference corrections to transport, which appear to subleading order in the number of scattering channels N, it is believed to correctly describe quantum transport to leading order in N. We here partially verify this belief, by comparing the predictions of the effective random matrix theory for the ensemble averages of polynomial functions of S and S^dagger of degree 2, 4, and 6 to a semiclassical calculation.