Ehrenfest time dependence of quantum transport corrections and spectral statistics

TL;DR

This paper investigates how the Ehrenfest time influences quantum transport corrections and spectral statistics in quantum dots, providing semiclassical calculations that align with field-theoretical results and highlighting the transition from classical to wave interference effects.

Contribution

It presents the first detailed semiclassical analysis of Ehrenfest time dependence on quantum corrections in transport and spectral statistics, confirming consistency with existing theoretical frameworks.

Findings

Ehrenfest time affects quantum corrections to transmission and reflection.

Results are consistent with current conservation and previous field-theoretical calculations.

The study links semiclassical and field-theoretical approaches in quantum chaos.

Abstract

The Ehrenfest time scale in quantum transport separates essentially classical propagation from wave interference and here we consider its effect on the transmission and reflection through quantum dots. In particular we calculate the Ehrenfest time dependence of the next-to-leading-order quantum corrections to the transmission and reflection for dc and ac transport and check that our results are consistent with current conservation relations. Looking as well at closed systems, we finally demonstrate how the contributions analyzed here imply changes in the calculation given in [P. W. Brouwer, S. Rahav and C. Tian, Phys. Rev. E, 74, 066208 (2006)] of the next to leading order of the spectral form factor. Our semiclassical result coincides with the result obtained in [C. Tian and A. I. Larkin, Phys. Rev. B, 70, 035305 (2004)] by field-theoretical methods.