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

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

2006-06-14

arxiv.org/abs/cond-mat/0606384v1

Phys. Rev. B 74, 085313 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

18 pages, 9 figures

Scientific paper

10.1103/PhysRevB.74.085313

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.

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