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

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.

18 pages, 9 figures

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Cited by in corpus (6)

• Lifetime statistics in chaotic dielectric microresonators
• Semiclassical theory of the Ehrenfest-time dependence of quantum transport
• Anderson localization from classical trajectories
• The spectral form factor near the Ehrenfest-time
• Semiclassical theory of a quantum pump
• Magnetic-field symmetries of mesoscopic nonlinear conductance